Precalculus Examples

$\frac{6}{2 x + 11} + 5 = 5$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

$\frac{6}{2 x + 11} = 5 - 5$

Step 1.2

Subtract $5$ from $5$ .

$\frac{6}{2 x + 11} = 0$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 x + 11, 1$

Step 2.2

Remove parentheses.

$2 x + 11, 1$

Step 2.3

The LCM of one and any expression is the expression.

$2 x + 11$

Step 3

Multiply each term in $\frac{6}{2 x + 11} = 0$ by $2 x + 11$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{6}{2 x + 11} = 0$ by $2 x + 11$ .

$\frac{6}{2 x + 11} (2 x + 11) = 0 (2 x + 11)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2 x + 11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6}{2 x + 11} (2 x + 11) = 0 (2 x + 11)$

Step 3.2.1.2

Rewrite the expression.

$6 = 0 (2 x + 11)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $0$ by $2 x + 11$ .

$6 = 0$

Step 4

Since $6 \neq 0$ , there are no solutions.

No solution