Find the LCD (4x+20)/(x^2+2x-15)

$\frac{4 x + 20}{x^{2} + 2 x - 15}$

Step 1

Factor $4$ out of $4 x + 20$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 20}{x^{2} + 2 x - 15}$

Factor $4$ out of $20$ .

$\frac{4 x + 4 \cdot 5}{x^{2} + 2 x - 15}$

Factor $4$ out of $4 x + 4 \cdot 5$ .

$\frac{4 (x + 5)}{x^{2} + 2 x - 15}$

Step 2

Factor $x^{2} + 2 x - 15$ 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 $2$ .

$- 3, 5$

Write the factored form using these integers.

$\frac{4 (x + 5)}{(x - 3) (x + 5)}$

Step 3

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{4 (x + 5)}{(x - 3) (x + 5)}$

Rewrite the expression.

$\frac{4}{x - 3}$

Step 4

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

$x - 3$

Step 5

Remove parentheses.

$x - 3$

Find the LCD (4x+20)/(x^2+2x-15)

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