Simplify (x^2-2x)/(x^2+3x-10)+(x-5)/(x+5)

$\frac{x^{2} - 2 x}{x^{2} + 3 x - 10} + \frac{x - 5}{x + 5}$

Step 1

Simplify each term.

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

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

$\frac{x \cdot x - 2 x}{x^{2} + 3 x - 10} + \frac{x - 5}{x + 5}$

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

$\frac{x \cdot x + x \cdot - 2}{x^{2} + 3 x - 10} + \frac{x - 5}{x + 5}$

Factor $x$ out of $x \cdot x + x \cdot - 2$ .

$\frac{x (x - 2)}{x^{2} + 3 x - 10} + \frac{x - 5}{x + 5}$

Factor $x^{2} + 3 x - 10$ 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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Write the factored form using these integers.

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

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{x + 5} + \frac{x - 5}{x + 5}$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$\frac{x + x - 5}{x + 5}$

Add $x$ and $x$ .

$\frac{2 x - 5}{x + 5}$

Simplify (x^2-2x)/(x^2+3x-10)+(x-5)/(x+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.