Algebra Examples

$\frac{(7 y - 3 x) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1

Cancel the common factor of $7 y - 3 x$ and $3 x - 7 y$ .

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Step 1.1

Factor $- 1$ out of $7 y$ .

$\frac{(- (- 7 y) - 3 x) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.2

Factor $- 1$ out of $- 3 x$ .

$\frac{(- (- 7 y) - (3 x)) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.3

Factor $- 1$ out of $- (- 7 y) - (3 x)$ .

$\frac{- (- 7 y + 3 x) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.4

Rewrite $- (- 7 y + 3 x)$ as $- 1 (- 7 y + 3 x)$ .

$\frac{- 1 (- 7 y + 3 x) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.5

Reorder terms.

$\frac{- 1 (3 x - 7 y) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.6

Cancel the common factor.

$\frac{- 1 (3 x - 7 y) (5 x - 1)}{(5 x^{3} + x^{2}) (3 x - 7 y)}$

Step 1.7

Rewrite the expression.

$\frac{- 1 (5 x - 1)}{5 x^{3} + x^{2}}$

Step 2

Factor $x^{2}$ out of $5 x^{3} + x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $5 x^{3}$ .

$\frac{- 1 (5 x - 1)}{x^{2} (5 x) + x^{2}}$

Step 2.2

Multiply by $1$ .

$\frac{- 1 (5 x - 1)}{x^{2} (5 x) + x^{2} \cdot 1}$

Step 2.3

Factor $x^{2}$ out of $x^{2} (5 x) + x^{2} \cdot 1$ .

$\frac{- 1 (5 x - 1)}{x^{2} (5 x + 1)}$

Step 3

Move the negative in front of the fraction.

$- \frac{5 x - 1}{x^{2} (5 x + 1)}$