Algebra Examples

$f (x) = \frac{2 x^{2} + 7 x}{x - 2}$

Step 1

Set $\frac{2 x^{2} + 7 x}{x - 2}$ equal to $0$ .

$\frac{2 x^{2} + 7 x}{x - 2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$2 x^{2} + 7 x = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Factor $x$ out of $2 x^{2} + 7 x$ .

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Step 2.2.1.1

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

$x (2 x) + 7 x = 0$

Step 2.2.1.2

Factor $x$ out of $7 x$ .

$x (2 x) + x \cdot 7 = 0$

Step 2.2.1.3

Factor $x$ out of $x (2 x) + x \cdot 7$ .

$x (2 x + 7) = 0$

Step 2.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$2 x + 7 = 0$

Step 2.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.4

Set $2 x + 7$ equal to $0$ and solve for $x$ .

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Step 2.2.4.1

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Step 2.2.4.2

Solve $2 x + 7 = 0$ for $x$ .

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Step 2.2.4.2.1

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Step 2.2.4.2.2

Divide each term in $2 x = - 7$ by $2$ and simplify.

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Step 2.2.4.2.2.1

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Step 2.2.4.2.2.2

Simplify the left side.

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Step 2.2.4.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.4.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Step 2.2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Step 2.2.4.2.2.3

Simplify the right side.

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Step 2.2.4.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 2.2.5

The final solution is all the values that make $x (2 x + 7) = 0$ true.

$x = 0, - \frac{7}{2}$

Step 3