How to divide rational expressions

Practice Questions

ACT Math › How to divide rational expressions

Questions

10

1

Simplify the expression, leaving no radicals in the denominator:

$\frac{7-\sqrt{13}}{5 +\sqrt{13}}$

2

Simplify the expression, leaving no radicals in the denominator:

$\frac{\sqrt{18}-\sqrt{5}}{3 -\sqrt{5}}$

3

Simplify the following expression:

$\frac{x^2+2x-3}{x^2-2x+1}\div \frac{3x+9}{3x-3}$

4

Simplify the expression:

$\frac{(4)\cdot(3x-24)}{(6x-48)\cdot(2x)}$

5

Simplify:

$\frac{(-5)\cdot(5x+30)}{(-x-6)\cdot(5x)}$

6

Which of the following is equivalent to $\dpi{100} \frac{(\frac{1}{t}-\frac{1}{x})}{x-t}$ ? Assume that denominators are always nonzero.

7

What is $\frac{x^{2} + 11x + 28}{x+7}$ ?

8

Simplify the expression:

$\frac{(3ab-9ax)}{(9a^2b-27a^2x)}$

9

Simplify the expression, leaving no radicals in the denominator:

$\frac{3+\sqrt{2}}{3 -\sqrt{3}}$

10

Simplify:

$\frac{x^{2}+x-2}{3x^{2} + 9x + 6} \div (x-1)$

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