amanf

2021-09-23

Solve rational equation.
$2-\frac{3}{y}=\frac{5}{{y}^{2}}$

Arnold Odonnell

Step 1
LCD is ${y}^{2}$
We multiply both sides by LCD and distribute it
$2-\frac{3}{y}=\frac{5}{{y}^{2}}$
Or, ${y}^{2}\left(2-\frac{3}{y}\right)={y}^{2}\frac{5}{{y}^{2}}$
Or, $2{y}^{2}-3y=5$
Step 2
Make right side equal to 0 and factor the left side
$2{y}^{2}-3y=5$
Or, $2{y}^{2}-3y-5=0$
Or, $2{y}^{2}-5y+2y-5=0$
Or, y(2y-5)+1(2y-5)=0
Or, (2y-5)(y+1)=0
Step 3
Set each factor equal to 0 and find y.
Answer: $y=\frac{5}{2}$ or -1
2y-5=0
Or, 2y=5
Or, $y=\frac{5}{2}$
y+1=0
Or, y=-1

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