Simplify (x-7)/(-5x+40)*(x^2-64)/(-4x+28)

$\frac{x - 7}{- 5 x + 40} \cdot \frac{x^{2} - 64}{- 4 x + 28}$

Step 1

Factor $5$ out of $- 5 x + 40$ .

Factor $5$ out of $- 5 x$ .

$\frac{x - 7}{5 (- x) + 40} \cdot \frac{x^{2} - 64}{- 4 x + 28}$

Factor $5$ out of $40$ .

$\frac{x - 7}{5 (- x) + 5 (8)} \cdot \frac{x^{2} - 64}{- 4 x + 28}$

Factor $5$ out of $5 (- x) + 5 (8)$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{x^{2} - 64}{- 4 x + 28}$

Step 2

Simplify the numerator.

Rewrite $64$ as $8^{2}$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{x^{2} - 8^{2}}{- 4 x + 28}$

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 $b = 8$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{(x + 8) (x - 8)}{- 4 x + 28}$

Step 3

Factor $4$ out of $- 4 x + 28$ .

Factor $4$ out of $- 4 x$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{(x + 8) (x - 8)}{4 (- x) + 28}$

Factor $4$ out of $28$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{(x + 8) (x - 8)}{4 (- x) + 4 (7)}$

Factor $4$ out of $4 (- x) + 4 (7)$ .

$\frac{x - 7}{5 (- x + 8)} \cdot \frac{(x + 8) (x - 8)}{4 (- x + 7)}$

Step 4

Multiply $\frac{x - 7}{5 (- x + 8)} \cdot \frac{(x + 8) (x - 8)}{4 (- x + 7)}$ .

Multiply $\frac{x - 7}{5 (- x + 8)}$ by $\frac{(x + 8) (x - 8)}{4 (- x + 7)}$ .

$\frac{(x - 7) ((x + 8) (x - 8))}{5 (- x + 8) (4 (- x + 7))}$

Multiply $4$ by $5$ .

$\frac{(x - 7) ((x + 8) (x - 8))}{20 (- x + 8) (- x + 7)}$

Step 5

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - 7$ and $- x + 7$ .

Factor $- 1$ out of $x$ .

$\frac{(- 1 (- x) - 7) ((x + 8) (x - 8))}{20 (- x + 8) (- x + 7)}$

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{(- 1 (- x) - 1 (7)) ((x + 8) (x - 8))}{20 (- x + 8) (- x + 7)}$

Factor $- 1$ out of $- 1 (- x) - 1 (7)$ .

$\frac{- 1 (- x + 7) ((x + 8) (x - 8))}{20 (- x + 8) (- x + 7)}$

Cancel the common factor.

$\frac{- 1 (- x + 7) ((x + 8) (x - 8))}{20 (- x + 8) (- x + 7)}$

Rewrite the expression.

$\frac{- 1 ((x + 8) (x - 8))}{20 (- x + 8)}$

Cancel the common factor of $x - 8$ and $- x + 8$ .

Factor $- 1$ out of $x$ .

$\frac{- 1 ((x + 8) (- 1 (- x) - 8))}{20 (- x + 8)}$

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{- 1 ((x + 8) (- 1 (- x) - 1 (8)))}{20 (- x + 8)}$

Factor $- 1$ out of $- 1 (- x) - 1 (8)$ .

$\frac{- 1 ((x + 8) (- 1 (- x + 8)))}{20 (- x + 8)}$

Cancel the common factor.

$\frac{- 1 (x + 8) (- 1 (- x + 8))}{20 (- x + 8)}$

Rewrite the expression.

$\frac{- 1 (x + 8) \cdot (- 1)}{20}$

Step 6

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$\frac{1 (x + 8)}{20}$

Multiply $x + 8$ by $1$ .

$\frac{x + 8}{20}$

Simplify (x-7)/(-5x+40)*(x^2-64)/(-4x+28)

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