Solve y=5x^2+4x-1/x+1-x^2-3x/x

$$y = \frac { 5 x ^ { 2 } + 4 x - 1 } { x + 1 } - \frac { x ^ { 2 } - 3 x } { x }$$

Solve for y

$$y=4x+2$$

$$x\neq -1\text{ and }x\neq 0$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x^{2}+4x-1}{x+1}.

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

Cancel out x+1 in both numerator and denominator.

$$y=5x-1-\frac{x^{2}-3x}{x}$$

Factor the expressions that are not already factored in \frac{x^{2}-3x}{x}.

$$y=5x-1-\frac{x\left(x-3\right)}{x}$$

Cancel out x in both numerator and denominator.

$$y=5x-1-\left(x-3\right)$$

To find the opposite of x-3, find the opposite of each term.

$$y=5x-1-x+3$$

Combine 5x and -x to get 4x.

$$y=4x-1+3$$

Add -1 and 3 to get 2.

$$y=4x+2$$

Solve for x (complex solution)

$$x=\frac{y-2}{4}$$

$$y\neq -2\text{ and }y\neq 2$$

Solve for x

$$x=\frac{y-2}{4}$$

$$|y|\neq 2$$