Simplify (3x^2-19x-14)/(5x^2+7x+2)*(5x+2)/(5x-35)

$\frac{3 x^{2} - 19 x - 14}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

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 $a \cdot c = 3 \cdot - 14 = - 42$ and whose sum is $b = - 19$ .

Factor $- 19$ out of $- 19 x$ .

$\frac{3 x^{2} - 19 (x) - 14}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Rewrite $- 19$ as $2$ plus $- 21$

$\frac{3 x^{2} + (2 - 21) x - 14}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Apply the distributive property.

$\frac{3 x^{2} + 2 x - 21 x - 14}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x^{2} + 2 x) - 21 x - 14}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

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

$\frac{x (3 x + 2) - 7 (3 x + 2)}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

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

$\frac{(3 x + 2) (x - 7)}{5 x^{2} + 7 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

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 $b = 7$ .

Factor $7$ out of $7 x$ .

$\frac{(3 x + 2) (x - 7)}{5 x^{2} + 7 (x) + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Rewrite $7$ as $2$ plus $5$

$\frac{(3 x + 2) (x - 7)}{5 x^{2} + (2 + 5) x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Apply the distributive property.

$\frac{(3 x + 2) (x - 7)}{5 x^{2} + 2 x + 5 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(3 x + 2) (x - 7)}{(5 x^{2} + 2 x) + 5 x + 2} \cdot \frac{5 x + 2}{5 x - 35}$

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

$\frac{(3 x + 2) (x - 7)}{x (5 x + 2) + 1 (5 x + 2)} \cdot \frac{5 x + 2}{5 x - 35}$

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

$\frac{(3 x + 2) (x - 7)}{(5 x + 2) (x + 1)} \cdot \frac{5 x + 2}{5 x - 35}$

Factor $5$ out of $5 x - 35$ .

Factor $5$ out of $5 x$ .

$\frac{(3 x + 2) (x - 7)}{(5 x + 2) (x + 1)} \cdot \frac{5 x + 2}{5 (x) - 35}$

Factor $5$ out of $- 35$ .

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

Factor $5$ out of $5 x + 5 \cdot - 7$ .

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

Cancel the common factor of $x - 7$ .

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

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

Factor $x - 7$ out of $5 (x - 7)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5 x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move $5$ to the left of $x + 1$ .

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

Simplify (3x^2-19x-14)/(5x^2+7x+2)*(5x+2)/(5x-35)

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