Simplify 1/(x^2-5x)+3/(x^2+2x-35)

$\frac{1}{x^{2} - 5 x} + \frac{3}{x^{2} + 2 x - 35}$

Simplify each term.

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

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

$\frac{1}{x \cdot x - 5 x} + \frac{3}{x^{2} + 2 x - 35}$

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

$\frac{1}{x \cdot x + x \cdot - 5} + \frac{3}{x^{2} + 2 x - 35}$

Factor $x$ out of $x \cdot x + x \cdot - 5$ .

$\frac{1}{x (x - 5)} + \frac{3}{x^{2} + 2 x - 35}$

Factor $x^{2} + 2 x - 35$ 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 $- 35$ and whose sum is $2$ .

$- 5, 7$

Write the factored form using these integers.

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

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

$\frac{1}{x (x - 5)} \cdot \frac{x + 7}{x + 7} + \frac{3}{(x - 5) (x + 7)}$

To write $\frac{3}{(x - 5) (x + 7)}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{x (x - 5)} \cdot \frac{x + 7}{x + 7} + \frac{3}{(x - 5) (x + 7)} \cdot \frac{x}{x}$

Write each expression with a common denominator of $x (x - 5) (x + 7)$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x + 7}{x (x - 5) (x + 7)} + \frac{3}{(x - 5) (x + 7)} \cdot \frac{x}{x}$

Multiply $\frac{3}{(x - 5) (x + 7)}$ by $\frac{x}{x}$ .

$\frac{x + 7}{x (x - 5) (x + 7)} + \frac{3 x}{(x - 5) (x + 7) x}$

Reorder the factors of $x (x - 5) (x + 7)$ .

$\frac{x + 7}{x (x + 7) (x - 5)} + \frac{3 x}{(x - 5) (x + 7) x}$

Reorder the factors of $(x - 5) (x + 7) x$ .

$\frac{x + 7}{x (x + 7) (x - 5)} + \frac{3 x}{x (x + 7) (x - 5)}$

Combine the numerators over the common denominator.

$\frac{x + 7 + 3 x}{x (x + 7) (x - 5)}$

Add $x$ and $3 x$ .

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

Simplify 1/(x^2-5x)+3/(x^2+2x-35)

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