Question 242743
{{{(y-3)/(y-6)-(y+1)/(y+6)+(y-42)/(y^2-36)}}} Start with the given expression.



{{{(y-3)/(y-6)-(y+1)/(y+6)+(y-42)/((y-6)(y+6))}}} Factor the last denominator.



Take note that the LCD is {{{(y-6)(y+6)}}}



{{{((y-3)(y+6))/((y-6)(y+6))-(y+1)/(y+6)+(y-42)/((y-6)(y+6))}}} Multiply the first fraction by {{{(y+6)/(y+6)}}} to get that denominator equal to the LCD.



{{{((y-3)(y+6))/((y-6)(y+6))-((y+1)(y-6))/((y-6)(y+6))+(y-42)/((y-6)(y+6))}}} Multiply the second fraction by {{{(y-6)/(y-6)}}} to get that denominator equal to the LCD.



{{{(y^2+3y-18)/((y-6)(y+6))-(y^2-5y-6)/((y-6)(y+6))+(y-42)/((y-6)(y+6))}}} FOIL.



{{{(y^2+3y-18-(y^2-5y-6)+(y-42))/((y-6)(y+6))}}} Combine the fractions.



{{{(y^2+3y-18-y^2+5y+6+y-42)/((y-6)(y+6))}}} Distribute.



{{{(9y-54)/((y-6)(y+6))}}} Combine like terms.



{{{(9(y-6))/((y-6)(y+6))}}} Factor the numerator.



{{{(9cross((y-6)))/(cross((y-6))(y+6))}}} Cancel out the common terms.



{{{9/(y+6)}}} Simplify.



So {{{(y-3)/(y-6)-(y+1)/(y+6)+(y-42)/(y^2-36)=9/(y+6)}}} where {{{y<>-6}}} or {{{y<>6}}}