Step 1
Given;
[tex]\begin{gathered} \frac{-5y-3}{30x^2+20}=\frac{z}{60x^2+40} \\ \text{where;} \\ z\text{ is the missing part of the equivalent rational }expression \end{gathered}[/tex]
Required; To find the missing part of the equivalent rational expression.
Step 2
Cross multiply
[tex]\begin{gathered} \frac{-5y-3}{30x^2+20}=\frac{z}{60x^2+40} \\ z(30x^2+20)=(-5y-3)(60x^2+40) \\ \end{gathered}[/tex]
Factorize 60x²+40
[tex]z(30x^2+20)=(-5y-3)(2(30x^2+20))[/tex]
Divide all through by 30x²+20
[tex]\begin{gathered} \frac{z(30x^2+20)}{(30x^2+20)}=\frac{(-5y-3)(2(30x^2+20))}{(30x^2+20)} \\ z=2(-5y-3) \\ z=-10y-6 \end{gathered}[/tex]
Hence;
[tex]\begin{gathered} \frac{-5y-3}{30x^2+20}=\frac{-10y-6}{60x^2+40} \\ \text{Therefore, the missing part of the equivalent rational expression is;} \\ -10y-6 \end{gathered}[/tex]
