Solve for x 15/(x+7)=x+5

$\frac{15}{x + 7} = x + 5$

Find the LCD of the terms in the equation.

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

$x + 7, 1, 1$

Remove parentheses.

$x + 7, 1, 1$

The LCM of one and any expression is the expression.

$x + 7$

Multiply each term in $\frac{15}{x + 7} = x + 5$ by $x + 7$ to eliminate the fractions.

Multiply each term in $\frac{15}{x + 7} = x + 5$ by $x + 7$ .

$\frac{15}{x + 7} (x + 7) = x (x + 7) + 5 (x + 7)$

Simplify the left side.

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{15}{x + 7} (x + 7) = x (x + 7) + 5 (x + 7)$

Rewrite the expression.

$15 = x (x + 7) + 5 (x + 7)$

Simplify the right side.

Simplify each term.

Apply the distributive property.

$15 = x \cdot x + x \cdot 7 + 5 (x + 7)$

Multiply $x$ by $x$ .

$15 = x^{2} + x \cdot 7 + 5 (x + 7)$

Move $7$ to the left of $x$ .

$15 = x^{2} + 7 \cdot x + 5 (x + 7)$

Apply the distributive property.

$15 = x^{2} + 7 x + 5 x + 5 \cdot 7$

Multiply $5$ by $7$ .

$15 = x^{2} + 7 x + 5 x + 35$

Add $7 x$ and $5 x$ .

$15 = x^{2} + 12 x + 35$

Solve the equation.

Rewrite the equation as $x^{2} + 12 x + 35 = 15$ .

$x^{2} + 12 x + 35 = 15$

Subtract $15$ from both sides of the equation.

$x^{2} + 12 x + 35 - 15 = 0$

Subtract $15$ from $35$ .

$x^{2} + 12 x + 20 = 0$

Factor $x^{2} + 12 x + 20$ using the AC method.

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 $20$ and whose sum is $12$ .

$2, 10$

Write the factored form using these integers.

$(x + 2) (x + 10) = 0$

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

$x + 2 = 0$

$x + 10 = 0$

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $x + 10$ equal to $0$ and solve for $x$ .

Set $x + 10$ equal to $0$ .

$x + 10 = 0$

Subtract $10$ from both sides of the equation.

$x = - 10$

The final solution is all the values that make $(x + 2) (x + 10) = 0$ true.

$x = - 2, - 10$

Solve for x 15/(x+7)=x+5

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