3x/x+6-x/x+5=2

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Solution

Given, 3x/x+6 - x/x+5 = 2

3x(x+5) - x(x+6)/(x+6)(x+5) = 2

3x^2 + 15x - x^2 - 6x/x^2 + 5x + 6x + 11 = 2

2x^2 + 9x = 2x^2 + 22x + 60

2x^2 + 9x - 2x^2 - 22x - 60

9x - 22x = 60

-13x = 60

x = -60/13.

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Similar questions

Solve the following equation :

$\frac{3 x}{x + 6} - \frac{x}{x + 5} = 2$

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x + 6 - 3 x - 5 - 2 (x - 5) = 2 x - 9 - 2 x + 5 - 3 (x + 1)

Q. The equation

\frac{(x + 2) (x - 5)}{(x - 3) (x + 6)} = \frac{x - 2}{x + 4}

has

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$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

I. (3x-2)/y=(3x+6)/(y+16)
II. (x+2)/(y+4)=(x+5)/(y+10)

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3x/x+6-x/x+5=2

Given, 3x/x+6 - x/x+5 = 2 3x(x+5) - x(x+6)/(x+6)(x+5) = 2 3x^2 + 15x - x^2 - 6x/x^2 + 5x + 6x + 11 = 2 2x^2 + 9x = 2x^2 + 22x + 60 2x^2 + 9x - 2x^2 - 22x - 60 9x - 22x = 60 -13x = 60 x = -60/13.

Given, 3x/x+6 - x/x+5 = 2

3x(x+5) - x(x+6)/(x+6)(x+5) = 2

3x^2 + 15x - x^2 - 6x/x^2 + 5x + 6x + 11 = 2

2x^2 + 9x = 2x^2 + 22x + 60

2x^2 + 9x - 2x^2 - 22x - 60

9x - 22x = 60

-13x = 60

x = -60/13.