Pre-Algebra Examples

$\frac{x (x - 2)}{x + 1} + 1 = \frac{31}{x + 1}$

Step 1

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

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Step 1.1

Combine into one fraction.

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Step 1.1.1

Write $1$ as a fraction with a common denominator.

$\frac{x (x - 2)}{x + 1} + \frac{x + 1}{x + 1} = \frac{31}{x + 1}$

Step 1.1.2

Combine the numerators over the common denominator.

$\frac{x (x - 2) + x + 1}{x + 1} = \frac{31}{x + 1}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 2 + x + 1}{x + 1} = \frac{31}{x + 1}$

Step 1.2.2

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot - 2 + x + 1}{x + 1} = \frac{31}{x + 1}$

Step 1.2.3

Move $- 2$ to the left of $x$ .

$\frac{x^{2} - 2 \cdot x + x + 1}{x + 1} = \frac{31}{x + 1}$

Step 1.2.4

Add $- 2 x$ and $x$ .

$\frac{x^{2} - x + 1}{x + 1} = \frac{31}{x + 1}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 5, 6$

Step 3