Simplify (6x^2+11x-2)/(4x^2-3x-1)*(5x^2-3x-2)/(3x^2+7x+2)

$\frac{6 x^{2} + 11 x - 2}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

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 $a \cdot c = 6 \cdot - 2 = - 12$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$\frac{6 x^{2} + 11 (x) - 2}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Rewrite $11$ as $- 1$ plus $12$

$\frac{6 x^{2} + (- 1 + 12) x - 2}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Apply the distributive property.

$\frac{6 x^{2} - 1 x + 12 x - 2}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x^{2} - 1 x) + 12 x - 2}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

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

$\frac{x (6 x - 1) + 2 (6 x - 1)}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Factor the polynomial by factoring out the greatest common factor, $6 x - 1$ .

$\frac{(6 x - 1) (x + 2)}{4 x^{2} - 3 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

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 $a \cdot c = 4 \cdot - 1 = - 4$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$\frac{(6 x - 1) (x + 2)}{4 x^{2} - 3 (x) - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Rewrite $- 3$ as $1$ plus $- 4$

$\frac{(6 x - 1) (x + 2)}{4 x^{2} + (1 - 4) x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Apply the distributive property.

$\frac{(6 x - 1) (x + 2)}{4 x^{2} + 1 x - 4 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Multiply $x$ by $1$ .

$\frac{(6 x - 1) (x + 2)}{4 x^{2} + x - 4 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x - 1) (x + 2)}{(4 x^{2} + x) - 4 x - 1} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

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

$\frac{(6 x - 1) (x + 2)}{x (4 x + 1) - (4 x + 1)} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{5 x^{2} - 3 x - 2}{3 x^{2} + 7 x + 2}$

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 $a \cdot c = 5 \cdot - 2 = - 10$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{5 x^{2} - 3 (x) - 2}{3 x^{2} + 7 x + 2}$

Rewrite $- 3$ as $2$ plus $- 5$

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{5 x^{2} + (2 - 5) x - 2}{3 x^{2} + 7 x + 2}$

Apply the distributive property.

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{5 x^{2} + 2 x - 5 x - 2}{3 x^{2} + 7 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x^{2} + 2 x) - 5 x - 2}{3 x^{2} + 7 x + 2}$

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

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{x (5 x + 2) - (5 x + 2)}{3 x^{2} + 7 x + 2}$

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x^{2} + 7 x + 2}$

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 $a \cdot c = 3 \cdot 2 = 6$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x^{2} + 7 (x) + 2}$

Rewrite $7$ as $1$ plus $6$

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x^{2} + (1 + 6) x + 2}$

Apply the distributive property.

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x^{2} + 1 x + 6 x + 2}$

Multiply $x$ by $1$ .

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x^{2} + x + 6 x + 2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{(3 x^{2} + x) + 6 x + 2}$

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

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{x (3 x + 1) + 2 (3 x + 1)}$

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

$\frac{(6 x - 1) (x + 2)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{(3 x + 1) (x + 2)}$

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(6 x - 1) (x + 2)$ .

$\frac{(x + 2) (6 x - 1)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{(3 x + 1) (x + 2)}$

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

$\frac{(x + 2) (6 x - 1)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{(x + 2) (3 x + 1)}$

Cancel the common factor.

$\frac{(x + 2) (6 x - 1)}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{(x + 2) (3 x + 1)}$

Rewrite the expression.

$\frac{6 x - 1}{(4 x + 1) (x - 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x + 1}$

Cancel the common factor of $x - 1$ .

Factor $x - 1$ out of $(4 x + 1) (x - 1)$ .

$\frac{6 x - 1}{(x - 1) (4 x + 1)} \cdot \frac{(5 x + 2) (x - 1)}{3 x + 1}$

Factor $x - 1$ out of $(5 x + 2) (x - 1)$ .

$\frac{6 x - 1}{(x - 1) (4 x + 1)} \cdot \frac{(x - 1) (5 x + 2)}{3 x + 1}$

Cancel the common factor.

$\frac{6 x - 1}{(x - 1) (4 x + 1)} \cdot \frac{(x - 1) (5 x + 2)}{3 x + 1}$

Rewrite the expression.

$\frac{6 x - 1}{4 x + 1} \cdot \frac{5 x + 2}{3 x + 1}$

Multiply $\frac{6 x - 1}{4 x + 1}$ by $\frac{5 x + 2}{3 x + 1}$ .

$\frac{(6 x - 1) (5 x + 2)}{(4 x + 1) (3 x + 1)}$

Simplify (6x^2+11x-2)/(4x^2-3x-1)*(5x^2-3x-2)/(3x^2+7x+2)

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