( y + 2 ) / y = 1 / ( y - 5 ) y+2y=1y−5
Then:
1 * y = ( y + 2 ) * ( y - 5 ) 1⋅y=(y+2)⋅(y−5)
So:
y = y^2 - 5y + 2y - 10 = y^2 - 3y - 10 y=y2−5y+2y−10=y2−3y−10
Unifying:
y^2 - 4y - 10 = 0 y2−4y−10=0
As we know in:
a*y^2 + b*y + c = 0 a⋅y2+b⋅y+c=0 ,
y = ( -b +- sqrt( b^2 -4*a*c ) ) / ( 2 * a ) y=−b±√b2−4⋅a⋅c2⋅a
So:
y = ( 4 +- sqrt( (-4)^2 -4*1*(-10) ) ) / ( 2 * 1 ) y=4±√(−4)2−4⋅1⋅(−10)2⋅1
y = ( 4 +- sqrt( 16 + 40 ) ) / 2 = ( 4 +- sqrt( 56 ) ) / 2 = 2 +- sqrt( 56 ) / 2 = y=4±√16+402=4±√562=2±√562=
y = 2 +- sqrt( 14 * 4 ) / 2 = 2 +- 2 / 2 * sqrt( 14 ) = 2 +- sqrt( 14 ) y=2±√14⋅42=2±22⋅√14=2±√14