Basic Math Examples

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

Step 1

Rewrite $7$ as $- 1 (- 7)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

Move a negative from the denominator of $\frac{7}{- 1 (- 7 + 5 y)}$ to the numerator.

$\frac{5 y}{5 y - 7} + \frac{- 1 \cdot 7}{- 7 + 5 y}$

Step 4.2

Reorder terms.

$\frac{5 y}{5 y - 7} + \frac{- 1 \cdot 7}{5 y - 7}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 y - 1 \cdot 7}{5 y - 7}$

Step 6

Multiply $- 1$ by $7$ .

$\frac{5 y - 7}{5 y - 7}$

Step 7

Cancel the common factor of $5 y - 7$ .

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Step 7.1

Cancel the common factor.

$\frac{5 y - 7}{5 y - 7}$

Step 7.2

Rewrite the expression.

$1$