Algebra Examples

$\frac{- 4 x}{- \frac{5}{y} + \frac{7}{x}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $- \frac{5}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{- 4 x}{- \frac{5}{y} \cdot \frac{x}{x} + \frac{7}{x}}$

Step 1.2

To write $\frac{7}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{- 4 x}{- \frac{5}{y} \cdot \frac{x}{x} + \frac{7}{x} \cdot \frac{y}{y}}$

Step 1.3

Write each expression with a common denominator of $y x$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{5}{y}$ by $\frac{x}{x}$ .

$\frac{- 4 x}{- \frac{5 x}{y x} + \frac{7}{x} \cdot \frac{y}{y}}$

Step 1.3.2

Multiply $\frac{7}{x}$ by $\frac{y}{y}$ .

$\frac{- 4 x}{- \frac{5 x}{y x} + \frac{7 y}{x y}}$

Step 1.3.3

Reorder the factors of $y x$ .

$\frac{- 4 x}{- \frac{5 x}{x y} + \frac{7 y}{x y}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- 4 x}{\frac{- 5 x + 7 y}{x y}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$- 4 x \frac{x y}{- 5 x + 7 y}$

Step 3

Multiply $- 4 x \frac{x y}{- 5 x + 7 y}$ .

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Step 3.1

Combine $- 4$ and $\frac{x y}{- 5 x + 7 y}$ .

$x \frac{- 4 (x y)}{- 5 x + 7 y}$

Step 3.2

Combine $x$ and $\frac{- 4 (x y)}{- 5 x + 7 y}$ .

$\frac{x (- 4 (x y))}{- 5 x + 7 y}$

Step 3.3

Raise $x$ to the power of $1$ .

$\frac{- 4 (x^{1} x y)}{- 5 x + 7 y}$

Step 3.4

Raise $x$ to the power of $1$ .

$\frac{- 4 (x^{1} x^{1} y)}{- 5 x + 7 y}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 4 (x^{1 + 1} y)}{- 5 x + 7 y}$

Step 3.6

Add $1$ and $1$ .

$\frac{- 4 (x^{2} y)}{- 5 x + 7 y}$

Step 4

Move the negative in front of the fraction.

$- \frac{4 x^{2} y}{- 5 x + 7 y}$

Step 5

Factor $- 1$ out of $- 5 x$ .

$- \frac{4 x^{2} y}{- (5 x) + 7 y}$

Step 6

Factor $- 1$ out of $7 y$ .

$- \frac{4 x^{2} y}{- (5 x) - (- 7 y)}$

Step 7

Factor $- 1$ out of $- (5 x) - (- 7 y)$ .

$- \frac{4 x^{2} y}{- (5 x - 7 y)}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (5 x - 7 y)$ as $- 1 (5 x - 7 y)$ .

$- \frac{4 x^{2} y}{- 1 (5 x - 7 y)}$

Step 8.2

Move the negative in front of the fraction.

$- - \frac{4 x^{2} y}{5 x - 7 y}$

Step 8.3

Multiply $- 1$ by $- 1$ .

$1 \frac{4 x^{2} y}{5 x - 7 y}$

Step 8.4

Multiply $\frac{4 x^{2} y}{5 x - 7 y}$ by $1$ .

$\frac{4 x^{2} y}{5 x - 7 y}$