Solve for x (x^2-3x-10)/(x^2-8x+15)=3

$\frac{x^{2} - 3 x - 10}{x^{2} - 8 x + 15} = 3$

Factor each term.

Factor $x^{2} - 3 x - 10$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$\frac{(x - 5) (x + 2)}{x^{2} - 8 x + 15} = 3$

Factor $x^{2} - 8 x + 15$ 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Write the factored form using these integers.

$\frac{(x - 5) (x + 2)}{(x - 5) (x - 3)} = 3$

Reduce the expression $\frac{(x - 5) (x + 2)}{(x - 5) (x - 3)}$ by cancelling the common factors.

Cancel the common factor.

$\frac{(x - 5) (x + 2)}{(x - 5) (x - 3)} = 3$

Rewrite the expression.

$\frac{x + 2}{x - 3} = 3$

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.

$x - 3, 1$

Remove parentheses.

$x - 3, 1$

The LCM of one and any expression is the expression.

$x - 3$

Multiply each term in $\frac{x + 2}{x - 3} = 3$ by $x - 3$ to eliminate the fractions.

Multiply each term in $\frac{x + 2}{x - 3} = 3$ by $x - 3$ .

$\frac{x + 2}{x - 3} (x - 3) = 3 (x - 3)$

Simplify the left side.

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{x + 2}{x - 3} (x - 3) = 3 (x - 3)$

Rewrite the expression.

$x + 2 = 3 (x - 3)$

Simplify the right side.

Apply the distributive property.

$x + 2 = 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$x + 2 = 3 x - 9$

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$x + 2 - 3 x = - 9$

Subtract $3 x$ from $x$ .

$- 2 x + 2 = - 9$

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

Subtract $2$ from both sides of the equation.

$- 2 x = - 9 - 2$

Subtract $2$ from $- 9$ .

$- 2 x = - 11$

Divide each term in $- 2 x = - 11$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 11$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 11}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 11}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{11}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}$

Decimal Form:

$x = 5.5$

Mixed Number Form:

$x = 5 \frac{1}{2}$

Solve for x (x^2-3x-10)/(x^2-8x+15)=3

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