Pre-Algebra Examples

$\frac{4 x - y}{16 x^{2} + 8 x y + y^{2}} \div \frac{1}{{(4 x + y)}^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 x - y}{16 x^{2} + 8 x y + y^{2}} {(4 x + y)}^{2}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\frac{4 x - y}{{(4 x)}^{2} + 8 x y + y^{2}} {(4 x + y)}^{2}$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x y = 2 \cdot (4 x) \cdot y$

Step 2.3

Rewrite the polynomial.

$\frac{4 x - y}{{(4 x)}^{2} + 2 \cdot (4 x) \cdot y + y^{2}} {(4 x + y)}^{2}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 4 x$ and $b = y$ .

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

Step 3

Cancel the common factor of ${(4 x + y)}^{2}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$4 x - y$