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


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

Solving Rational equations. LCD method. Show work. Image attached. (5k)/(k+2) + (2)/(k-example-1

1 Answer

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Answer:


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)

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