Question

$\frac{6m}{m + 1}+\frac{4m}{5m + 3}
\frac{am^{2}+bm}{(m + 1)(5m + 3)}
a=

b=$

Explanation:

Step1: Find a common - denominator

Since the common denominator of $\frac{6m}{m + 1}$ and $\frac{4m}{5m+3}$ is $(m + 1)(5m+3)$, we rewrite the fractions: $\frac{6m(5m + 3)}{(m + 1)(5m+3)}+\frac{4m(m + 1)}{(m + 1)(5m+3)}$.

Step2: Expand the numerators

$6m(5m + 3)=30m^{2}+18m$ and $4m(m + 1)=4m^{2}+4m$.

Step3: Add the numerators

$(30m^{2}+18m)+(4m^{2}+4m)=30m^{2}+4m^{2}+18m + 4m=34m^{2}+22m$.

Step4: Compare with the given form

Comparing $34m^{2}+22m$ with $Am^{2}+Bm$, we get $A = 34$ and $B=22$.

Answer:

$A = 34$
$B = 22$