Answer:
[tex]k=\frac{1}{2}[/tex]
Step-by-step explanation:
The given rational equation is
[tex]\frac{5k}{k+2}+\frac{2}{k}=5[/tex]
The Least Common Denominator is
[tex]k(k+2)[/tex]
Multiply each term by the LCD.
[tex]k(k+2)\times \frac{5k}{k+2}+k(k+2)\times \frac{2}{k}=5k(k+2)[/tex]
Simplify;
[tex]k\times \frac{5k}{1}+(k+2)\times \frac{2}{1}=5k(k+2)[/tex]
[tex]\Rightarrow k(5k)+2(k+2)=5k(k+2)[/tex]
Expand;
[tex]\Rightarrow 5k^2+2k+4=5k^2+10k[/tex]
Group similar terms;
[tex]\Rightarrow 5k^2-5k^2+2k-10k=-4[/tex]
[tex]\Rightarrow -8k=-4[/tex]
Divide by -8.
[tex]k=\frac{1}{2}[/tex]
