Simplify (3x)/(x^2+3x-28)-(2x)/(x^2+x-20)

$\frac{3 x}{x^{2} + 3 x - 28} - \frac{2 x}{x^{2} + x - 20}$

Simplify each term.

Factor $x^{2} + 3 x - 28$ 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 $- 28$ and whose sum is $3$ .

$- 4, 7$

Write the factored form using these integers.

$\frac{3 x}{(x - 4) (x + 7)} - \frac{2 x}{x^{2} + x - 20}$

Factor $x^{2} + x - 20$ 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 $1$ .

$- 4, 5$

Write the factored form using these integers.

$\frac{3 x}{(x - 4) (x + 7)} - \frac{2 x}{(x - 4) (x + 5)}$

To write $\frac{3 x}{(x - 4) (x + 7)}$ as a fraction with a common denominator, multiply by $\frac{x + 5}{x + 5}$ .

$\frac{3 x}{(x - 4) (x + 7)} \cdot \frac{x + 5}{x + 5} - \frac{2 x}{(x - 4) (x + 5)}$

To write $- \frac{2 x}{(x - 4) (x + 5)}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{3 x}{(x - 4) (x + 7)} \cdot \frac{x + 5}{x + 5} - \frac{2 x}{(x - 4) (x + 5)} \cdot \frac{x + 7}{x + 7}$

Write each expression with a common denominator of $(x - 4) (x + 7) (x + 5)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{(x - 4) (x + 7)}$ by $\frac{x + 5}{x + 5}$ .

$\frac{3 x (x + 5)}{(x - 4) (x + 7) (x + 5)} - \frac{2 x}{(x - 4) (x + 5)} \cdot \frac{x + 7}{x + 7}$

Multiply $\frac{2 x}{(x - 4) (x + 5)}$ by $\frac{x + 7}{x + 7}$ .

$\frac{3 x (x + 5)}{(x - 4) (x + 7) (x + 5)} - \frac{2 x (x + 7)}{(x - 4) (x + 5) (x + 7)}$

Reorder the factors of $(x - 4) (x + 7) (x + 5)$ .

$\frac{3 x (x + 5)}{(x + 5) (x + 7) (x - 4)} - \frac{2 x (x + 7)}{(x - 4) (x + 5) (x + 7)}$

Reorder the factors of $(x - 4) (x + 5) (x + 7)$ .

$\frac{3 x (x + 5)}{(x + 5) (x + 7) (x - 4)} - \frac{2 x (x + 7)}{(x + 5) (x + 7) (x - 4)}$

Combine the numerators over the common denominator.

$\frac{3 x (x + 5) - 2 x (x + 7)}{(x + 5) (x + 7) (x - 4)}$

Simplify the numerator.

Factor $x$ out of $3 x (x + 5) - 2 x (x + 7)$ .

Factor $x$ out of $3 x (x + 5)$ .

$\frac{x (3 (x + 5)) - 2 x (x + 7)}{(x + 5) (x + 7) (x - 4)}$

Factor $x$ out of $- 2 x (x + 7)$ .

$\frac{x (3 (x + 5)) + x (- 2 (x + 7))}{(x + 5) (x + 7) (x - 4)}$

Factor $x$ out of $x (3 (x + 5)) + x (- 2 (x + 7))$ .

$\frac{x (3 (x + 5) - 2 (x + 7))}{(x + 5) (x + 7) (x - 4)}$

Apply the distributive property.

$\frac{x (3 x + 3 \cdot 5 - 2 (x + 7))}{(x + 5) (x + 7) (x - 4)}$

Multiply $3$ by $5$ .

$\frac{x (3 x + 15 - 2 (x + 7))}{(x + 5) (x + 7) (x - 4)}$

Apply the distributive property.

$\frac{x (3 x + 15 - 2 x - 2 \cdot 7)}{(x + 5) (x + 7) (x - 4)}$

Multiply $- 2$ by $7$ .

$\frac{x (3 x + 15 - 2 x - 14)}{(x + 5) (x + 7) (x - 4)}$

Subtract $2 x$ from $3 x$ .

$\frac{x (x + 15 - 14)}{(x + 5) (x + 7) (x - 4)}$

Subtract $14$ from $15$ .

$\frac{x (x + 1)}{(x + 5) (x + 7) (x - 4)}$

Simplify (3x)/(x^2+3x-28)-(2x)/(x^2+x-20)

Related Questions

Support LCMGCF.com by disabling your adblocker.