Chapter 12, Problem 9CCSR

To determine

To find: the expression which is equivalent to the $\frac{4x^2-9}{6x^2+9x}$ .

Answer to Problem 9CCSR

The option D is correct option.

Explanation of Solution

Given:

  $\frac{4x^2-9}{6x^2+9x}$ .

Concept used:

The equation can be expanded by multiplying the number outside the bracket and inside the bracket.

Same or like term can be added or subtracted combining together will form new equation.

The higher degree of the polynomial should be written first.

Using algebraic identities:

  $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Calculation:

  $\frac{4x^2-9}{6x^2+9x}$ .

The equation can be taken common as:

Using algebraic identities:

  $\begin{array}{l}{a}^2-b^2=\left(a+b\right)\left(a-b\right).\\ \frac{4x^2-9}{6x^2+9x}\Rightarrow \frac{{\left(2x\right)}^2-{\left(3\right)}^2}{3x.\left(2x+3\right)}\\ \Rightarrow \frac{\left(2x+3\right).\left(2x-3\right)}{3x\left(2x+3\right)}.\\ \Rightarrow \frac{\left(2x-3\right)}{3x}.\end{array}$

Hence, option D is correct option.