Chapter 11.4, Problem 12MCQ

To determine

Multiply or divide $\frac{4d^2-3d}{7d}÷\left(4d^2+d-3\right)$

Answer to Problem 12MCQ

The solution of the given equation is $\frac{4d^2-3d}{28d^3+7d^2-21d}$

Explanation of Solution

Given:

Given equation

  $\frac{4d^2-3d}{7d}÷\left(4d^2+d-3\right)$

Concept Used:

• Least Common Denominator (LCD) is the smallest number that is divisible by the denominator of all the fractions that are being added or subtracted.
• Solving an equation containing rational expressions
1. Multiply both sides of equations by LCD(least common denominator) of all denominators.
2. Remove any grouping symbols and solve the resulting equation for the variable asked in equation

Calculation:

In order to solve the equation $\frac{4d^2-3d}{7d}÷\left(4d^2+d-3\right)$ , observe that it is function of divide, so simplify further as shown below

  $\begin{array}{c}\frac{4d^2-3d}{7d}÷\left(4d^2+d-3\right)=\frac{\frac{4d^2-3d}{7d}}{\left(4d^2+d-3\right)}\\ =\frac{4d^2-3d}{7d}\times \frac{1}{\left(4d^2+d-3\right)}\\ =\frac{\left(4d^2-3d\right)\cdot 1}{\left(7d\right)\cdot \left(4d^2+d-3\right)}\\ =\frac{4d^2-3d}{7d\left(4d^2+d-3\right)}\\ =\frac{4d^2-3d}{\left(7d\cdot 4d^2+7d\cdot d-7d\cdot 3\right)}\\ =\frac{4d^2-3d}{28d^3+7d^2-21d}\end{array}$

Thus, the solution of the given equation is $\frac{4d^2-3d}{28d^3+7d^2-21d}$