Question

Divide the first expression by the second. Write the quotient and the remainder.

$x^2-\frac{1}{4x^2};x-\frac{1}{2x}$

• A. Quotient = $x+\frac{2}{2x}$, Remainder = 1
• B. Quotient = $2x+\frac{1}{2x}$, Remainder = 0
• C. Quotient = $x-\frac{1}{2x}$, Remainder = 1
• D. Quotient = $x+\frac{1}{2x}$, Remainder = 0

Answer 1

The correct option is D Quotient = $x+\frac{1}{2x}$, Remainder = 0

First expression $=x^2-\frac{1}{4x^2}=(x+\frac{1}{2x})(x-\frac{1}{2x})$

Second expression $=x-\frac{1}{2x}$

When $(x+\frac{1}{2x})(x-\frac{1}{2x})$ is divided by $x-\frac{1}{2x}$

Quotient $=x+\frac{1}{2x}$, Remainder $=0$