Perform the indicated operations y8y ly 7y 6 y 1y8y 76y

Perform the indicated operations. (y-8)(y + l)/(y + 7)(y -6) - (y + 1)(y+8)/(y + 7)(6-y) (y + 9)(y-7)/(y + 7)(6-y)

Solution

( y-8)(y +1)/( x +7)( y-6) - ( y+1)(y+8)/( y+7))( 6-y) - ( y+9)( y-7)/(y +7)( 6-y)

Ist IInd IIIrd

we can write IInd as: -( y+1)(y+8)/( y+7))( y-6)

we can write IIIrd as: - ( y+9)( y-7)/(y +7)( y-6)

So,( y-8)(y +1)/( y +7)( y-6) + ( y+1)(y+8)/( y+7))( y-6) +( y+9)( y-7)/(y +7)( y-6)

= 1/( y +7)( y-6) { ( y-8)( y+1) + (y+1)( y+8) + ( y+9)( y-7) }

=1/( y +7)( y-6) { 2y(y+1) +(y+9)(y-7) }

=1/( y +7)( y-6) { 2y^2 + 2y +y^2 + 2y - 63 }

=1/( y +7)( y-6) { 3y^2 +4y -63 }

= ( 3y^2 +4y -63)/( y+7)(y -6)