Simplify x/(x^2-3x-4)+(2x)/(x-4)

$\frac{x}{x^{2} - 3 x - 4} + \frac{2 x}{x - 4}$

Factor $x^{2} - 3 x - 4$ 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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Write the factored form using these integers.

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

To write $\frac{2 x}{x - 4}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

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

Simplify terms.

Multiply $\frac{2 x}{x - 4}$ by $\frac{x + 1}{x + 1}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $x + 2 x (x + 1)$ .

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $2 x (x + 1)$ .

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

Factor $x$ out of $x \cdot 1 + x (2 (x + 1))$ .

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

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

Add $1$ and $2$ .

$\frac{x (2 x + 3)}{(x - 4) (x + 1)}$

Simplify x/(x^2-3x-4)+(2x)/(x-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.