Solve the equationSolution1 given 13x 15x4 14x take the 15

Solve the equation

1) . given 13/x -15/(x+4) = 14/x

take the -15/(x+4) to the right hand side, and bring 14/x to left hand side

13/x -14/x = 15/(x+4)

-1/x = 15/(x+4)

-(x+4) = 15x ( cross multiplying)

-x -4 =15x

16x =-4

so x=-1/4

2).

5x/(x+2) +6 = 1/(x+2)

take 6 to the right hand side , bring 1/(x+2) to the left hand side

5x/(x+2) -1/(x+2) =-6

(5x-1) /(x+2) =-6

(5x-1) =-6(x+2)

5x-1 =-6x-12

11x =-12+1

x=-1

3).

given x+64/x =-20

(x^2 +64) / x =-20

(x^2 +64) = -20x

x^2 +20x+64=0

x^2 +16x+4x+64=0

x(x+16) +4(x+16)=0

(x+4) (x+16) =0

so x=-4 or x=-16

x = -4, -16

4).

(4x) /(3x+2) + (6x+1) /(x+5) = (2x-9)/(3x^2 +17x+10)

[ (4x) (x+5) + ((6x+1) (3x+2) ] / (3x^2 +17x+10) =(2x-9)/(3x^2 +17x+10)

4x^2 +20x +18x^2+ 15x+12 = 2x-9

22x^2 +33x +21=0

x=-0.75