Question

Rewrite the rational expression as an equivalent rational expression whose denominator is the given polynomial

Answer 1

Step 1

Given;

`\begin{gathered} (-5y-3)/(30x^2+20)=(z)/(60x^2+40) \\ \text{where;} \\ z\text{ is the missing part of the equivalent rational }expression \end{gathered}`

Required; To find the missing part of the equivalent rational expression.

Step 2

Cross multiply

`\begin{gathered} (-5y-3)/(30x^2+20)=(z)/(60x^2+40) \\ z(30x^2+20)=(-5y-3)(60x^2+40) \\ \end{gathered}`

Factorize 60x²+40

`z(30x^2+20)=(-5y-3)(2(30x^2+20))`

Divide all through by 30x²+20

`\begin{gathered} (z(30x^2+20))/((30x^2+20))=((-5y-3)(2(30x^2+20)))/((30x^2+20)) \\ z=2(-5y-3) \\ z=-10y-6 \end{gathered}`

Hence;

`\begin{gathered} (-5y-3)/(30x^2+20)=(-10y-6)/(60x^2+40) \\ \text{Therefore, the missing part of the equivalent rational expression is;} \\ -10y-6 \end{gathered}`