Question

1. $\frac{4}{3a^{2}-6a}-\frac{2}{3a - 6}$

Explanation:

Step1: Factor the denominators

Factor $3a^{2}-6a = 3a(a - 2)$ and $3a-6=3(a - 2)$.

Step2: Find the common - denominator

The common denominator of $\frac{4}{3a(a - 2)}$ and $\frac{2}{3(a - 2)}$ is $3a(a - 2)$.

Step3: Rewrite the fractions with the common denominator

$\frac{4}{3a(a - 2)}-\frac{2\times a}{3(a - 2)\times a}=\frac{4}{3a(a - 2)}-\frac{2a}{3a(a - 2)}$.

Step4: Subtract the numerators

$\frac{4-2a}{3a(a - 2)}=\frac{-2(a - 2)}{3a(a - 2)}$.

Step5: Simplify the fraction

Cancel out the common factor $(a - 2)$ (assuming $a
eq2$), we get $-\frac{2}{3a}$.

Answer:

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