Precalculus Examples

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

Step 1

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

$- \frac{3}{2} \cdot \frac{y - 3}{y - 3} + \frac{3}{y - 3}$

Step 2

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

$- \frac{3}{2} \cdot \frac{y - 3}{y - 3} + \frac{3}{y - 3} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $2 (y - 3)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{2}$ by $\frac{y - 3}{y - 3}$ .

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

Step 3.2

Multiply $\frac{3}{y - 3}$ by $\frac{2}{2}$ .

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

Step 3.3

Reorder the factors of $(y - 3) \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

Factor $3$ out of $- 3 (y - 3)$ .

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

Step 5.1.2

Factor $3$ out of $3 \cdot 2$ .

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

Step 5.1.3

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

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Multiply $- 1$ by $- 3$ .

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

Step 5.4

Add $3$ and $2$ .

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

Step 6

Simplify with factoring out.

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Step 6.1

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

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

Step 6.2

Rewrite $5$ as $- 1 (- 5)$ .

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

Step 6.3

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

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

Step 6.4

Simplify the expression.

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Step 6.4.1

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

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

Step 6.4.2

Move the negative in front of the fraction.

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

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