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Thepotemich [5.8K]
2 years ago
11

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

Mathematics
1 answer:
Ugo [173]2 years ago
5 0

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}

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