Algebra Examples

$\frac{x^{2} + 10 x - 11}{x - 11}$

Step 1

Set $\frac{x^{2} + 10 x - 11}{x - 11}$ equal to $0$ .

$\frac{x^{2} + 10 x - 11}{x - 11} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$x^{2} + 10 x - 11 = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Factor $x^{2} + 10 x - 11$ using the AC method.

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Step 2.2.1.1

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 $- 11$ and whose sum is $10$ .

$- 1, 11$

Step 2.2.1.2

Write the factored form using these integers.

$(x - 1) (x + 11) = 0$

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 $0$ .

$x - 1 = 0$

$x + 11 = 0$

Step 2.2.3

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 2.2.3.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.2.3.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.2.4

Set $x + 11$ equal to $0$ and solve for $x$ .

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Step 2.2.4.1

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Step 2.2.4.2

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 2.2.5

The final solution is all the values that make $(x - 1) (x + 11) = 0$ true.

$x = 1, - 11$

Step 3