Move expression to the left side and change its sign
5/(y-3)+10/(y^2-y-6)-y/(y+2)=05y−3+10y2−y−6−yy+2=0
Write -y−y as a sum or difference
5/(y-3)+10/(y^2+2y-3y-6)-y/(y+2)=05y−3+10y2+2y−3y−6−yy+2=0
Factor out yy and -3−3 from the expression
5/(y-3)+10/(y(y+2)-3(y+2))-y/(y+2)=05y−3+10y(y+2)−3(y+2)−yy+2=0
Factor out y+2y+2 from the expression
5/(y-3)+10/((y+2)(y-3))-y/(y+2)=05y−3+10(y+2)(y−3)−yy+2=0
Write all numerators above the least common denominator
(5(y+2)+10-y(y-3))/((y+2)(y-3))=05(y+2)+10−y(y−3)(y+2)(y−3)=0
Distribute 55 and -y−y through the parenthesis
(5y+10+10-y^2+3y)/((y+2)(y-3))=05y+10+10−y2+3y(y+2)(y−3)=0
Collect the like terms
(8y+20-y^2)/((y+2)(y-3))=08y+20−y2(y+2)(y−3)=0
Use the commutative property to reorder the terms
(-y^2+8y+20)/((y+2)(y-3))=0−y2+8y+20(y+2)(y−3)=0
Write 8y8y as a sum or difference
(-y^2+10y-2y+20)/((y+2)(y-3))=0−y2+10y−2y+20(y+2)(y−3)=0
Factor out -y−y and -2−2 from the expression
(-y(y-10)-2(y-10))/((y+2)(y-3))=0−y(y−10)−2(y−10)(y+2)(y−3)=0
Factor out -(y-10)−(y−10) from the expression
(-(y-10)(y+2))/((y+2)(y-3))=0−(y−10)(y+2)(y+2)(y−3)=0
Reduce the fraction with y+2y+2
-(y-10)/(y-3)=0−y−10y−3=0
Determine the sign of the fraction
-(y-10)/(y-3)=0−y−10y−3=0
Simplify
(10-y)/(y-3)=010−yy−3=0
When the quotient of expressions equals 00, the numerator has to be 00
10-y=010−y=0
Move the constant, 1010, to the right side and change its sign
-y=-10−y=−10
Change the signs on both sides of the equation
y=10y=10
Check if the solution is in the defined range
y=10, y!=3,y!=-2y=10,y≠3,y≠−2
:. y=10
