Basic Math Examples

$\frac{16 a^{2}}{4 a + 7 b} - \frac{49 b^{2}}{4 a + 7 b}$

Step 1

Combine the numerators over the common denominator.

$\frac{16 a^{2} - 49 b^{2}}{4 a + 7 b}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{{(4 a)}^{2} - 49 b^{2}}{4 a + 7 b}$

Step 2.2

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

$\frac{{(4 a)}^{2} - {(7 b)}^{2}}{4 a + 7 b}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 a$ and $b = 7 b$ .

$\frac{(4 a + 7 b) (4 a - (7 b))}{4 a + 7 b}$

Step 2.4

Multiply $7$ by $- 1$ .

$\frac{(4 a + 7 b) (4 a - 7 b)}{4 a + 7 b}$

Step 3

Cancel the common factor of $4 a + 7 b$ .

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Step 3.1

Cancel the common factor.

$\frac{(4 a + 7 b) (4 a - 7 b)}{4 a + 7 b}$

Step 3.2

Divide $4 a - 7 b$ by $1$ .

$4 a - 7 b$