Question

If $\frac{9x^2}{3x-2}$ $=A+\frac{4}{3x-2}$, find $A$ in terms of $x$?

• A. $\frac{9x^2}{4}$
• B. $3x+2$
• C. $3x-2$
• D. $9x^2-4$

Answer 1

Answer: (B)

$3x+2$

Isolate A: $\frac{9x^2}{3x-2}-\frac{4}{3x-2}=A$
Denominator are equal,
$\frac{9x^2-4}{3x-2}=A$
Expand $9x^2-4=(3x{)}^2-2^2=(3x+2\left)\right(3x-2)$
$A=\frac{(3x+2)(3x-2)}{3x-2}$
Therefore, $A=3x+2$