simplify 5/(m-1)-2/(m-3) — step-by-step solution

The original denominators must be nonzero:

m \in ℝ \ {1, 3}

Let's sum the fractions:

\frac{5}{m - 1} - \frac{2}{m - 3}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{5}{m - 1} - \frac{2}{m - 3}

\frac{5 \cdot (m - 3) - 2 \cdot (m - 1)}{(m - 1) \cdot (m - 3)}

\frac{5 \cdot (m - 3) - 2 \cdot (m - 1)}{(m - 1) \cdot (m - 3)}

ⓘ Expand by multiplying each term inside the parentheses:

5 \cdot (m - 3)

5 m - 15

- 2 \cdot (m - 1)

- (2 m - 2)

\frac{5 m - 15 - (2 m - 2)}{(m - 1) \cdot (m - 3)}

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (2 m - 2)

- 2 m + 2

\frac{5 m - 15 - 2 m + 2}{(m - 1) \cdot (m - 3)}

ⓘ The numerator and the denominator are computed before the division:

- 15 + 2

-13

■Like terms are grouped by adding their coefficients:

5 m - 2 m

3 m

▶Result:

\frac{3 m - 13}{(m - 1) \cdot (m - 3)}