Rational Expressions - GRE Quantitative Reasoning

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.

Therefore, is the best answer.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.

Therefore, is the best answer.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.

Therefore, is the best answer.

To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.

This is the most simplified version of the rational expression.

To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).