+0

# ​ Simplify.

0
220
2
+389

this the answer that I got

Mar 5, 2018

#1
+7354
+3

$$\quad\frac{\frac{x^2+x-12}{x-2}}{\frac{3x^2+11x-4}{x^2-4}}\\ =\\ \quad\frac{x^2+x-12}{x-2}\cdot\frac{x^2-4}{3x^2+11x-4} \\ =\\ \quad\frac{(x+4)(x-3)}{(x-2)}\cdot\frac{(x+2)(x-2)}{3x^2+12x-x-4} \\ =\\ \quad\frac{(x+4)(x-3)}{(x-2)}\cdot\frac{(x+2)(x-2)}{3x(x+4)-1(x+4)} \\ =\\ \quad\frac{(x+4)(x-3)}{(x-2)}\cdot\frac{(x+2)(x-2)}{(x+4)(3x-1)} \\ =\\ \quad\frac{(x+4)(x-3)(x+2)(x-2)}{(x-2)(x+4)(3x-1)} \\ =\\ \quad\frac{(x-3)(x+2)}{(3x-1)} \qquad\text{and}\qquad x\neq-4\, \qquad x\neq2\\ =\\ \quad\frac{x^2-x-6}{3x-1}$$

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Mar 5, 2018
#2
+68
+2

$$\frac{\frac{x^2+x-12}{x-2}}{\frac{3x^2+11x-4}{x^2-4}}$$

Simplify the polynomials.

$$\frac{\frac{(x+4)(x-3)}{x-2}}{\frac{(3x-1)(x+4)}{(x+2)(x-2)}}$$

Multiply the top and bottom fractions by (x+2)(x-2).

$$\frac{(x+4)(x-3)(x+2)}{(3x-1)(x+4)}$$

Cross out like terms.

$$\frac{(x-3)(x+2)}{(3x-1)}$$

Multiply the top polynomial out.

$$\frac{x^2-x+6}{3x-1}$$

Just a different way to look at it. :D

Mar 5, 2018