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

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

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

`(6x^3+ay^2)/(12xy)=b+y`

Cross multiply both sides, we will have

`\begin{gathered} (6x^3+ay^2)/(12xy)=(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 \\ (ay^2)/(y^2)=(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}=(6x^3)/(12xy) \\ b=(x^2)/(2y) \end{gathered}`

Hence,

The complete equation will be

`(6x^3+12xy^2)/(12xy)=(x^2)/(2y)+y`