Question

complete the equation to simplify the expression by filling in the blanks(6x^3+[ ]y^2)----------------- = [ ] + y12xy

Answer 1

The question is given below as

$\frac{6x^3+()y^2}{12xy}=\text{ ( ) + y}$

Now, we will have to replace the blank spaces with letters a and b

$\frac{6x^3+ay^2}{12xy}=b+y$

Cross multiply both sides, we will have

$\begin{gathered} \frac{6x^3+ay^2}{12xy}=\frac{b+y}{1} \\ 6x^3+ay^2=12\text{xyb}+12xy^2 \end{gathered}$

By comparing coefficients, we will have

$\begin{gathered} ay^2=12xy^2 \\ \text{divide both sides by y}^2 \\ \frac{ay^2}{y^2}=\frac{12xy^2}{y^2} \\ a=12x \end{gathered}$

By comparing the second coefficient, we will have

$\begin{gathered} 12\text{xyb}=6x^3 \\ \text{divide both sides by 12xy, we will have} \\ \frac{12\text{xyb}}{12xy}=\frac{6x^3}{12xy} \\ b=\frac{x^2}{2y} \end{gathered}$

Hence,

The complete equation will be

$\frac{6x^3+12xy^2}{12xy}=\frac{x^2}{2y}+y$