simplify (m-9)/(9m+3)+4/(7m^2) — step-by-step solution

The original denominators must be nonzero:

m \in ℝ \ {- \frac{1}{3}, 0}

Let's add fractions:

\frac{m - 9}{9 m + 3} + \frac{4}{7 m^{2}}

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

\frac{m - 9}{9 m + 3} + \frac{4}{7 m^{2}}

\frac{(m - 9) \cdot 7 m^{2} + 4 \cdot (9 m + 3)}{(9 m + 3) \cdot 7 m^{2}}

\frac{(m - 9) \cdot 7 m^{2} + 4 \cdot (9 m + 3)}{(9 m + 3) \cdot 7 m^{2}}

ⓘ Expand by multiplying each term inside the parentheses:

(m - 9) \cdot 7

m \cdot 7 - 63

4 \cdot (9 m + 3)

36 m + 12

\frac{(m \cdot 7 - 63) \cdot m^{2} + 36 m + 12}{(9 m + 3) \cdot 7 m^{2}}

ⓘ Expand by multiplying each term inside the parentheses:

(m \cdot 7 - 63) \cdot m^{2}

7 m^{3} - 63 m^{2}

\frac{7 m^{3} - 63 m^{2} + 36 m + 12}{(9 m + 3) \cdot 7 m^{2}}

▶Result:

\frac{7 m^{3} - 63 m^{2} + 36 m + 12}{7 m^{2} \cdot (9 m + 3)}