Question

The simplified form of the expression given below is :-

$\begin{array}{cc}& \underset{–}{y^4-x^4}-\underset{–}{y^3}\\ & \frac{x\left(x+y\right)x}{y^2-xy+x^2}\end{array}$

• A. $1$
• B. $0$
• C. $-1$
• D. $2$

Answer 1

The correct option is C $-1$

Solution :- given

$=\frac{\frac{y^4-x^4}{x(x+y)}-\frac{y^3}{x}}{y^2-xy+x^2}$

$=\frac{\frac{(y^4-x^4)-y^3(x+y)}{x(x+y)}}{x^2-xy+y^2}$

$=\frac{y^4-x^4-x{y}^3-y^4}{x(x+y)(x^2-xy+y^2)}$ We know $(a+b)(a^2-ab+b^2)=a^3+b^3$

$=\frac{-x(x^3+y^3)}{x(x^3+y^3)}$

$=-1$ (Ans)