Algebra Examples

$\frac{- 5 y}{2 y - 1} - \frac{y + 3}{2 y - 1}$

Step 1

Combine the numerators over the common denominator.

$\frac{- 5 y - (y + 3)}{2 y - 1}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{- 5 y - y - 1 \cdot 3}{2 y - 1}$

Step 2.2

Multiply $- 1$ by $3$ .

$\frac{- 5 y - y - 3}{2 y - 1}$

$\frac{- 5 y - y - 3}{2 y - 1}$

Step 3

Simplify terms.

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Step 3.1

Subtract $y$ from $- 5 y$ .

$\frac{- 6 y - 3}{2 y - 1}$

Step 3.2

Factor $3$ out of $- 6 y - 3$ .

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Step 3.2.1

Factor $3$ out of $- 6 y$ .

$\frac{3 (- 2 y) - 3}{2 y - 1}$

Step 3.2.2

Factor $3$ out of $- 3$ .

$\frac{3 (- 2 y) + 3 (- 1)}{2 y - 1}$

Step 3.2.3

Factor $3$ out of $3 (- 2 y) + 3 (- 1)$ .

$\frac{3 (- 2 y - 1)}{2 y - 1}$

$\frac{3 (- 2 y - 1)}{2 y - 1}$

Step 3.3

Factor $- 1$ out of $- 2 y$ .

$\frac{3 (- (2 y) - 1)}{2 y - 1}$

Step 3.4

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

$\frac{3 (- (2 y) - 1 (1))}{2 y - 1}$

Step 3.5

Factor $- 1$ out of $- (2 y) - 1 (1)$ .

$\frac{3 (- (2 y + 1))}{2 y - 1}$

Step 3.6

Simplify the expression.

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Step 3.6.1

Rewrite $- (2 y + 1)$ as $- 1 (2 y + 1)$ .

$\frac{3 (- 1 (2 y + 1))}{2 y - 1}$

Step 3.6.2

Move the negative in front of the fraction.

$- \frac{3 (2 y + 1)}{2 y - 1}$

$- \frac{3 (2 y + 1)}{2 y - 1}$

$- \frac{3 (2 y + 1)}{2 y - 1}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$