Basic Math Examples

\frac{3}{t - 2} - \frac{2}{2 t - 3}

$\frac{3}{t - 2} - \frac{2}{2 t - 3}$

Step 1

To write

\frac{3}{t - 2}

$\frac{3}{t - 2}$ as a fraction with a common denominator, multiply by

\frac{2 t - 3}{2 t - 3}

$\frac{2 t - 3}{2 t - 3}$ .

\frac{3}{t - 2} \cdot \frac{2 t - 3}{2 t - 3} - \frac{2}{2 t - 3}

$\frac{3}{t - 2} \cdot \frac{2 t - 3}{2 t - 3} - \frac{2}{2 t - 3}$

Step 2

To write

- \frac{2}{2 t - 3}

$- \frac{2}{2 t - 3}$ as a fraction with a common denominator, multiply by

\frac{t - 2}{t - 2}

$\frac{t - 2}{t - 2}$ .

\frac{3}{t - 2} \cdot \frac{2 t - 3}{2 t - 3} - \frac{2}{2 t - 3} \cdot \frac{t - 2}{t - 2}

$\frac{3}{t - 2} \cdot \frac{2 t - 3}{2 t - 3} - \frac{2}{2 t - 3} \cdot \frac{t - 2}{t - 2}$

Step 3

Write each expression with a common denominator of

(t - 2) (2 t - 3)

$(t - 2) (2 t - 3)$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{t - 2}

$\frac{3}{t - 2}$ by

\frac{2 t - 3}{2 t - 3}

$\frac{2 t - 3}{2 t - 3}$ .

\frac{3 (2 t - 3)}{(t - 2) (2 t - 3)} - \frac{2}{2 t - 3} \cdot \frac{t - 2}{t - 2}

$\frac{3 (2 t - 3)}{(t - 2) (2 t - 3)} - \frac{2}{2 t - 3} \cdot \frac{t - 2}{t - 2}$

Step 3.2

Multiply

\frac{2}{2 t - 3}

$\frac{2}{2 t - 3}$ by

\frac{t - 2}{t - 2}

$\frac{t - 2}{t - 2}$ .

\frac{3 (2 t - 3)}{(t - 2) (2 t - 3)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}

$\frac{3 (2 t - 3)}{(t - 2) (2 t - 3)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}$

Step 3.3

Reorder the factors of

(t - 2) (2 t - 3)

$(t - 2) (2 t - 3)$ .

\frac{3 (2 t - 3)}{(2 t - 3) (t - 2)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}

$\frac{3 (2 t - 3)}{(2 t - 3) (t - 2)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}$

\frac{3 (2 t - 3)}{(2 t - 3) (t - 2)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}

$\frac{3 (2 t - 3)}{(2 t - 3) (t - 2)} - \frac{2 (t - 2)}{(2 t - 3) (t - 2)}$

Step 4

Combine the numerators over the common denominator.

\frac{3 (2 t - 3) - 2 (t - 2)}{(2 t - 3) (t - 2)}

$\frac{3 (2 t - 3) - 2 (t - 2)}{(2 t - 3) (t - 2)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

\frac{3 (2 t) + 3 \cdot - 3 - 2 (t - 2)}{(2 t - 3) (t - 2)}

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

Step 5.2

Multiply

$2$ by

$3$ .

$\frac{6 t + 3 \cdot - 3 - 2 (t - 2)}{(2 t - 3) (t - 2)}$

Step 5.3

Multiply

$3$ by

$- 3$ .

$\frac{6 t - 9 - 2 (t - 2)}{(2 t - 3) (t - 2)}$

Step 5.4

Apply the distributive property.

$\frac{6 t - 9 - 2 t - 2 \cdot - 2}{(2 t - 3) (t - 2)}$

Step 5.5

Multiply

$- 2$ by

$- 2$ .

$\frac{6 t - 9 - 2 t + 4}{(2 t - 3) (t - 2)}$

Step 5.6

Subtract

$2 t$ from

$6 t$ .

$\frac{4 t - 9 + 4}{(2 t - 3) (t - 2)}$

Step 5.7

Add

$- 9$ and

$4$ .

$\frac{4 t - 5}{(2 t - 3) (t - 2)}$