Simplify (21x^2-2x-3)/(4x-12)*(x-3)/(49x^2-9)

$\frac{21 x^{2} - 2 x - 3}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Step 1

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 $a \cdot c = 21 \cdot - 3 = - 63$ and whose sum is $b = - 2$ .

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

$\frac{21 x^{2} - 2 (x) - 3}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Rewrite $- 2$ as $7$ plus $- 9$

$\frac{21 x^{2} + (7 - 9) x - 3}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Apply the distributive property.

$\frac{21 x^{2} + 7 x - 9 x - 3}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(21 x^{2} + 7 x) - 9 x - 3}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

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

$\frac{7 x (3 x + 1) - 3 (3 x + 1)}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

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

$\frac{(3 x + 1) (7 x - 3)}{4 x - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Step 2

Factor $4$ out of $4 x - 12$ .

Factor $4$ out of $4 x$ .

$\frac{(3 x + 1) (7 x - 3)}{4 (x) - 12} \cdot \frac{x - 3}{49 x^{2} - 9}$

Factor $4$ out of $- 12$ .

$\frac{(3 x + 1) (7 x - 3)}{4 x + 4 \cdot - 3} \cdot \frac{x - 3}{49 x^{2} - 9}$

Factor $4$ out of $4 x + 4 \cdot - 3$ .

$\frac{(3 x + 1) (7 x - 3)}{4 (x - 3)} \cdot \frac{x - 3}{49 x^{2} - 9}$

Step 3

Simplify the denominator.

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

$\frac{(3 x + 1) (7 x - 3)}{4 (x - 3)} \cdot \frac{x - 3}{{(7 x)}^{2} - 9}$

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 x$ and $b = 3$ .

$\frac{(3 x + 1) (7 x - 3)}{4 (x - 3)} \cdot \frac{x - 3}{(7 x + 3) (7 x - 3)}$

Step 4

Simplify terms.

Cancel the common factor of $7 x - 3$ .

Factor $7 x - 3$ out of $(3 x + 1) (7 x - 3)$ .

$\frac{(7 x - 3) (3 x + 1)}{4 (x - 3)} \cdot \frac{x - 3}{(7 x + 3) (7 x - 3)}$

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

$\frac{(7 x - 3) (3 x + 1)}{4 (x - 3)} \cdot \frac{x - 3}{(7 x - 3) (7 x + 3)}$

Cancel the common factor.

$\frac{(7 x - 3) (3 x + 1)}{4 (x - 3)} \cdot \frac{x - 3}{(7 x - 3) (7 x + 3)}$

Rewrite the expression.

$\frac{3 x + 1}{4 (x - 3)} \cdot \frac{x - 3}{7 x + 3}$

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $4 (x - 3)$ .

$\frac{3 x + 1}{(x - 3) \cdot 4} \cdot \frac{x - 3}{7 x + 3}$

Cancel the common factor.

$\frac{3 x + 1}{(x - 3) \cdot 4} \cdot \frac{x - 3}{7 x + 3}$

Rewrite the expression.

$\frac{3 x + 1}{4} \cdot \frac{1}{7 x + 3}$

Multiply $\frac{3 x + 1}{4}$ by $\frac{1}{7 x + 3}$ .

$\frac{3 x + 1}{4 (7 x + 3)}$

Simplify (21x^2-2x-3)/(4x-12)*(x-3)/(49x^2-9)

Related Questions

Support LCMGCF.com by disabling your adblocker.