Question

solve for x: 1/x+1 + 3/5x+1 = 5/x+4, x not equal to -1, -1/5,-4

Answer 1

1/x+1 + 3/5x+1 = 5/x+4

take lcm on lhs

5x+1+3x+3/(x+1)(5x+1)=5/x+4

8x+4/5x^2+x+5x+1=5/x+4

cross multiply

(8x+4)(x+4)=(5)(5x^2+6x+1)

8x^2+32x+4x+16=25x^2+30x+5

17x^2-6x-11=0

solve it

17x^2-17x+11x-11=0

17x(x-1)+11(x-1)=0

(17x+11)(x-1)

gives

x=1 or x=-11/17

hope this helps