Simplify (3x^2-3x)/(x^2+3x-4)*(x^2-16)/(3x^2)

$\frac{3 x^{2} - 3 x}{x^{2} + 3 x - 4} \cdot \frac{x^{2} - 16}{3 x^{2}}$

Step 1

Factor $3 x$ out of $3 x^{2} - 3 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$\frac{3 x (x) - 3 x}{x^{2} + 3 x - 4} \cdot \frac{x^{2} - 16}{3 x^{2}}$

Factor $3 x$ out of $- 3 x$ .

$\frac{3 x (x) + 3 x (- 1)}{x^{2} + 3 x - 4} \cdot \frac{x^{2} - 16}{3 x^{2}}$

Factor $3 x$ out of $3 x (x) + 3 x (- 1)$ .

$\frac{3 x (x - 1)}{x^{2} + 3 x - 4} \cdot \frac{x^{2} - 16}{3 x^{2}}$

Step 2

Factor $x^{2} + 3 x - 4$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

$\frac{3 x (x - 1)}{(x - 1) (x + 4)} \cdot \frac{x^{2} - 16}{3 x^{2}}$

Step 3

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

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

Step 4

Simplify terms.

Combine.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $(x (x - 1)) ((x + 4) (x - 4))$ .

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

Cancel the common factors.

Factor $x$ out of $(x - 1) (x + 4) (x^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{(x + 4) (x - 4)}{(x + 4) (x)}$

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{(x + 4) x}$

Rewrite the expression.

$\frac{x - 4}{x}$

Simplify (3x^2-3x)/(x^2+3x-4)*(x^2-16)/(3x^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.