Algebra give the common factors of the numerator and the denominator of the following rational expressions. 1. 4c/6c 2. 2xy/3x 3. 8a2c/-4ac2 4. -14abc/12ac 5. (-3r)(-4s)/-18r2

I interpreted the question as:

(x-2)/(4-x) + 2/3 = (x-2)/12 or

(x-2) 2 (x-2)
------ + --- = -----
(4-x) 3 12

Now to find a common denominator.

I factor all the terms and see what is common, so it can be eliminated to leave the lowest common denominator.

(4 - x) - prime - cannot be factored

3 - prime - cannot be factored

12 - 4 x 3

What is common in the above? The 3, so we can eliminate one 3.

Common denominator - (4 -x) (3)(4)

So, we must multiply the numerator and denominator of the first term by 12 (3 x 4).

The next term's numerator and denominator must be multiplied by 4(4-x).

The term on the right of the equals sign must have the numerator and denominator multiplied by (4-x).

Good luck.

If you need more assistance, post again.

Paul

I think you want to reduce the fraction to the lowest terms.

Improper fraction 1 3/4 produces an improper fraction of 7/4 (1 times denominator plus numerator)

To reduce a fraction, we need to divide the numerator (number on top) and the denominator (number on the bottom) by the greatest common factor (GCF).

To get the GCF, find the factors of the numerators and denominators and find the greatest number that is in both lists.

The factors of 2 are 1, 2.

The factors of 10 are 1, 2, 5, 10.

The greatest (largest) number is both lists is 2, so we divide the numerator and denominator by 2 and get 1/5.

Good luck,

Paul

Factor both the numerator and denominator, and then divide both the numerator and denominator by the greatest common factor.

For example, 1/3 + 1/6 = 2/6 + 1/6 = 3/6. We have to simplify 3/6. The factors of 3 are 3 and 1. The factors of 6 and 1, 2, 3, and 6. The greatest common factor is 3. Dividing the numerator and denominator by 3 results in 1/2.

Good luck.

Paul

A mixed number is a number composed of an integer (whole) number and a proper fraction, one that has a numerator less than the denominator. Example 2 1/3 =2+ 1/3. 2 is the integer part, and 1/3 is the proper fraction part.
Certain fractions can be simplified further because the numerator and denominator share a (common) factor. By cancelling the common factor in the numerator with the factor in the denominator,
one gets a fraction with smaller numerator and denominator.
For example the percentage you provide 0.15% can be converted to 15/10000.
Since 15 and 1000 are both multiples of 5, the number 5 is a common factor in both. 15=5*3, and 10000=5*2000
Cancel the two 5 (simplifying by 5) in numerator and denominator leaves 3/2000. Thus
0.15%= 0.15/100=0.0015=3/200
I hope that this makes sense to you.

It is not possible to give a general answer to such a question. If you have a fraction, simplifying it entails dividing by factors that are common to the denominator and the numerator. If you have an algebraic expression such as a polynomial you simplify it by combining like terms until you have only one term of each type. A trigonometric expression can be compacted, etc.

Unfortunately this calculator does not display results in radical form. If you enter SQRT(147) you get 12.12435565...
What you are asking for is called rationalizing an irrational expression. Usually one tries to get rid of radicals that appear in the denominators. Here is an example.
Suppose you have 1/(c+SQRT(d)), and you want to get rid of the radical in the denominator. How to do it?
Recall the identity (a-b)*(a+b)= a^2-b^2. It is true for any a and b

Rationalizing a denominator (usual case)
Now consider (c+SQRT(d)). Multiply it by (c-SQRT(d))
[c+SQRT(d)]*[c-SQRT(d)]=c^2 -[SQRT(d)]^2=c^2-d
You see that there is no radical.
Now take 1/(c+SQRT(d)). To get rid of the radical from the denominator multiply it by (c-SQRT(d)). But to leave the value of your expression 1/(c+SQRT(d)) unchanged, you must multiply both numerator and denominator by (c-SQRT(d)).
The numerator becomes 1*(c-SQRT(d))=c-SQRT(d), and the denominator (c^2-d).
Finally, the rationalized form of the expression 1/(c+SQRT(d)) is
[c-SQRT(d)]/[c^2-d].

Rationalizing a numerator
Sometimes, people have a radical in the numerator that they want to get rid of and have it in the denominator. The procedure is the same
Example:(c+SQRT(d)), the denominator here is 1
(c+SQRT(d))=(c+SQRT(d))*[c-SQRT(d)]/[c-SQRT(d)]. This gives
[c^2-d]/[c-SQRT(d)]
You have no radical in the numerator but there is one in the denominator. This is called rationalizing the numerator.
Your case is a lot simpler
SQRT(147)=7*SQRT(3)
Multiply it by SQRT(3)/SQRT(3) which is 1. This gives
SQRT(147)=7*3/SQRT(3)=21/SQRT(3)

SQRT(147)= 21/SQRT(3)

A rational number is that number which can take the form a/b where a and b are non zero integers.
The numerator can easily be divided by the denominator and you get an answer which is exhaustive.

For example 2/5 gives 0.4; 3/10 gives 0.333... this is also rational

This calculator cannot do algebra ( manipulating expressions with letter symbols) . It does not have a CAS (computer Algebra System). All it can do is evaluate (find the numerical value of) expressions typed in. If it has the appropriate keys to enter variables such as A,B,C, or X and Y., and you entered an expression with variables it will use the numerical values stored in the variables. If you have not stored anything in a variable, it is given the value 0 by default.

hi maybe the formula below will help you

A rational number is a number that can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. Fractions are written as two numbers, the numerator and the denominator, with a dividing bar between them. In the fraction written m⁄n or
m represents equal parts, where n equal parts of that size make up one whole. Two different fractions may correspond to the same rational number; for example 1⁄2 and 2⁄4 are equal, that is:
If the absolute value of m is greater than n, then the absolute value of the fraction is greater than 1. Fractions can be greater than, less than, or equal to 1 and can also be positive, negative, or zero. The set of all rational numbers includes the integers, since every integer can be written as a fraction with denominator 1. For example −7 can be written −7⁄1. The symbol for the rational numbers is Q (for quotient), also written .

Hello,
I will show you the steps. You should be able to carry them out.
1. Get rid of the 5 on the left by transferring it to the right, while obeying the rules.
2. Write the right side as a fraction with 16 as denominator.
3. Calculate 4^3.
4. Get rid of the number that multiply x by transferring to the right side, while obeying the rules.
5.Express the right hand side as a fraction reduced to its simplest form (Hint:a factor 16 will simplify).
6. Give the result as fraction or calculate its decimal value if that is what is asked.
Hope it helps.