Question

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

Answer 1

Answer:

$k=\frac{1}{2}$

Step-by-step explanation:

The given rational equation is

$\frac{5k}{k+2}+\frac{2}{k}=5$

The Least Common Denominator is

$k(k+2)$

Multiply each term by the LCD.

$k(k+2)\times \frac{5k}{k+2}+k(k+2)\times \frac{2}{k}=5k(k+2)$

Simplify;

$k\times \frac{5k}{1}+(k+2)\times \frac{2}{1}=5k(k+2)$

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

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.

$k=\frac{1}{2}$