Simplify (2x^2+7x-15)/(3x^2+16x+5)*(3x^2-2x-1)/(2x^2-x-3)

$\frac{2 x^{2} + 7 x - 15}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{2 x^{2} + 7 (x) - 15}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Rewrite $7$ as $- 3$ plus $10$

$\frac{2 x^{2} + (- 3 + 10) x - 15}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Apply the distributive property.

$\frac{2 x^{2} - 3 x + 10 x - 15}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x^{2} - 3 x) + 10 x - 15}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor (GCF) from each group.

$\frac{x (2 x - 3) + 5 (2 x - 3)}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$\frac{(2 x - 3) (x + 5)}{3 x^{2} + 16 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = 16$ .

Factor $16$ out of $16 x$ .

$\frac{(2 x - 3) (x + 5)}{3 x^{2} + 16 (x) + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Rewrite $16$ as $1$ plus $15$

$\frac{(2 x - 3) (x + 5)}{3 x^{2} + (1 + 15) x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Apply the distributive property.

$\frac{(2 x - 3) (x + 5)}{3 x^{2} + 1 x + 15 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Multiply $x$ by $1$ .

$\frac{(2 x - 3) (x + 5)}{3 x^{2} + x + 15 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x - 3) (x + 5)}{(3 x^{2} + x) + 15 x + 5} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(2 x - 3) (x + 5)}{x (3 x + 1) + 5 (3 x + 1)} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{3 x^{2} - 2 x - 1}{2 x^{2} - x - 3}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 1 = - 3$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 x$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{3 x^{2} - 2 (x) - 1}{2 x^{2} - x - 3}$

Rewrite $- 2$ as $1$ plus $- 3$

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{3 x^{2} + (1 - 3) x - 1}{2 x^{2} - x - 3}$

Apply the distributive property.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{3 x^{2} + 1 x - 3 x - 1}{2 x^{2} - x - 3}$

Multiply $x$ by $1$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{3 x^{2} + x - 3 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x^{2} + x) - 3 x - 1}{2 x^{2} - x - 3}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{x (3 x + 1) - (3 x + 1)}{2 x^{2} - x - 3}$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{2 x^{2} - x - 3}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{2 x^{2} - (x) - 3}$

Rewrite $- 1$ as $2$ plus $- 3$

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{2 x^{2} + (2 - 3) x - 3}$

Apply the distributive property.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{2 x^{2} + 2 x - 3 x - 3}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{(2 x^{2} + 2 x) - 3 x - 3}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{2 x (x + 1) - 3 (x + 1)}$

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{(x + 1) (2 x - 3)}$

Cancel the common factor of $2 x - 3$ .

Factor $2 x - 3$ out of $(x + 1) (2 x - 3)$ .

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{(2 x - 3) (x + 1)}$

Cancel the common factor.

$\frac{(2 x - 3) (x + 5)}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{(2 x - 3) (x + 1)}$

Rewrite the expression.

$\frac{x + 5}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{x + 1}$

Cancel the common factor of $3 x + 1$ .

Cancel the common factor.

$\frac{x + 5}{(3 x + 1) (x + 5)} \cdot \frac{(3 x + 1) (x - 1)}{x + 1}$

Rewrite the expression.

$\frac{x + 5}{x + 5} \cdot \frac{x - 1}{x + 1}$

Multiply $\frac{x + 5}{x + 5}$ by $\frac{x - 1}{x + 1}$ .

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

Cancel the common factor of $x + 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 1}{x + 1}$

Simplify (2x^2+7x-15)/(3x^2+16x+5)*(3x^2-2x-1)/(2x^2-x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.