Simplify (x+1)/(x(x-7))-5x/((x-7)(x+1))

$\frac{x + 1}{x (x - 7)} - 5 \frac{x}{(x - 7) (x + 1)}$

Simplify each term.

Combine $- 5$ and $\frac{x}{(x - 7) (x + 1)}$ .

$\frac{x + 1}{x (x - 7)} + \frac{- 5 x}{(x - 7) (x + 1)}$

Move the negative in front of the fraction.

$\frac{x + 1}{x (x - 7)} - \frac{5 x}{(x - 7) (x + 1)}$

To write $\frac{x + 1}{x (x - 7)}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{x + 1}{x (x - 7)} \cdot \frac{x + 1}{x + 1} - \frac{5 x}{(x - 7) (x + 1)}$

To write $- \frac{5 x}{(x - 7) (x + 1)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x + 1}{x (x - 7)} \cdot \frac{x + 1}{x + 1} - \frac{5 x}{(x - 7) (x + 1)} \cdot \frac{x}{x}$

Write each expression with a common denominator of $x (x - 7) (x + 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 1}{x (x - 7)}$ by $\frac{x + 1}{x + 1}$ .

$\frac{(x + 1) (x + 1)}{x (x - 7) (x + 1)} - \frac{5 x}{(x - 7) (x + 1)} \cdot \frac{x}{x}$

Multiply $\frac{5 x}{(x - 7) (x + 1)}$ by $\frac{x}{x}$ .

$\frac{(x + 1) (x + 1)}{x (x - 7) (x + 1)} - \frac{5 x \cdot x}{(x - 7) (x + 1) x}$

Reorder the factors of $x (x - 7) (x + 1)$ .

$\frac{(x + 1) (x + 1)}{x (x + 1) (x - 7)} - \frac{5 x \cdot x}{(x - 7) (x + 1) x}$

Reorder the factors of $(x - 7) (x + 1) x$ .

$\frac{(x + 1) (x + 1)}{x (x + 1) (x - 7)} - \frac{5 x \cdot x}{x (x + 1) (x - 7)}$

Combine the numerators over the common denominator.

$\frac{(x + 1) (x + 1) - 5 x \cdot x}{x (x + 1) (x - 7)}$

Simplify the numerator.

Expand $(x + 1) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$\frac{x (x + 1) + 1 (x + 1) - 5 x \cdot x}{x (x + 1) (x - 7)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot 1 + 1 (x + 1) - 5 x \cdot x}{x (x + 1) (x - 7)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1 - 5 x \cdot x}{x (x + 1) (x - 7)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Subtract $5 x^{2}$ from $x^{2}$ .

$\frac{- 4 x^{2} + 2 x + 1}{x (x + 1) (x - 7)}$

Simplify with factoring out.

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

$\frac{- (4 x^{2}) + 2 x + 1}{x (x + 1) (x - 7)}$

Factor $- 1$ out of $2 x$ .

$\frac{- (4 x^{2}) - (- 2 x) + 1}{x (x + 1) (x - 7)}$

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

$\frac{- (4 x^{2} - 2 x) + 1}{x (x + 1) (x - 7)}$

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

$\frac{- (4 x^{2} - 2 x) - 1 (- 1)}{x (x + 1) (x - 7)}$

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

$\frac{- (4 x^{2} - 2 x - 1)}{x (x + 1) (x - 7)}$

Simplify the expression.

Rewrite $- (4 x^{2} - 2 x - 1)$ as $- 1 (4 x^{2} - 2 x - 1)$ .

$\frac{- 1 (4 x^{2} - 2 x - 1)}{x (x + 1) (x - 7)}$

Move the negative in front of the fraction.

$- \frac{4 x^{2} - 2 x - 1}{x (x + 1) (x - 7)}$

Simplify (x+1)/(x(x-7))-5x/((x-7)(x+1))

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