(7x+34)/(x+1)=x+2

Solution for (7x+34)/(x+1)=x+2 equation:

D( x )

x+1 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:+oo)

(7*x+34)/(x+1) = x+2 // - x+2

(7*x+34)/(x+1)-x-2 = 0

(7*x+34)/(x+1)+(-x*(x+1))/(x+1)+(-2*(x+1))/(x+1) = 0

7*x-x*(x+1)-2*(x+1)+34 = 0

6*x-x^2-2*x-2+34 = 0

4*x-x^2+32 = 0

4*x-x^2+32 = 0

4*x-x^2+32 = 0

DELTA = 4^2-(-1*4*32)

DELTA = 144

DELTA > 0

x = (144^(1/2)-4)/(-1*2) or x = (-144^(1/2)-4)/(-1*2)

x = -4 or x = 8

(x+4)*(x-8) = 0

((x+4)*(x-8))/(x+1) = 0

((x+4)*(x-8))/(x+1) = 0 // * x+1

(x+4)*(x-8) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -4, 8 }