Question

Solving Rational equations. LCD method. Show work. Image attached.


`(5k)/(k+2) + (2)/(k) = 5`

Answer 1

`k=(1)/(2)`

Explanation:

The given rational equation is

`(5k)/(k+2)+(2)/(k)=5`

The Least Common Denominator is

`k(k+2)`

Multiply each term by the LCD.

`k(k+2)* (5k)/(k+2)+k(k+2)* (2)/(k)=5k(k+2)`

Simplify;

`k* (5k)/(1)+(k+2)* (2)/(1)=5k(k+2)`

`\Rightarrow k(5k)+2(k+2)=5k(k+2)`

Expand;

`\Rightarrow 5k^2+2k+4=5k^2+10k`

Group similar terms;

`\Rightarrow 5k^2-5k^2+2k-10k=-4`

`\Rightarrow -8k=-4`

Divide by -8.

`k=(1)/(2)`