Algebra Examples

$3 {(x + y)}^{- 1} + x^{- 2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.2

Combine $3$ and $\frac{1}{x + y}$ .

$\frac{3}{x + y} + x^{- 2}$

Step 1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{x + y} + \frac{1}{x^{2}}$

Step 2

To write $\frac{3}{x + y}$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{3}{x + y} \cdot \frac{x^{2}}{x^{2}} + \frac{1}{x^{2}}$

Step 3

To write $\frac{1}{x^{2}}$ as a fraction with a common denominator, multiply by $\frac{x + y}{x + y}$ .

$\frac{3}{x + y} \cdot \frac{x^{2}}{x^{2}} + \frac{1}{x^{2}} \cdot \frac{x + y}{x + y}$

Step 4

Write each expression with a common denominator of $(x + y) x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{x + y}$ by $\frac{x^{2}}{x^{2}}$ .

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

Step 4.2

Multiply $\frac{1}{x^{2}}$ by $\frac{x + y}{x + y}$ .

$\frac{3 x^{2}}{(x + y) x^{2}} + \frac{x + y}{x^{2} (x + y)}$

Step 4.3

Reorder the factors of $(x + y) x^{2}$ .

$\frac{3 x^{2}}{x^{2} (x + y)} + \frac{x + y}{x^{2} (x + y)}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 x^{2} + x + y}{x^{2} (x + y)}$