Simplify (x+4)/(3x^2+11x-4)

$\frac{x + 4}{3 x^{2} + 11 x - 4}$

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 $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$\frac{x + 4}{3 x^{2} + 11 (x) - 4}$

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

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

Apply the distributive property.

$\frac{x + 4}{3 x^{2} - 1 x + 12 x - 4}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Step 2

Cancel the common factor of $x + 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3 x - 1}$

Simplify (x+4)/(3x^2+11x-4)

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