What is the answer to 3x+1=((5x+2))/a+((x-1))/b ?

The answer to 3x+1=((5x+2))/a+((x-1))/b is x=(2b-a-ab)/(3ab-5b-a);\quad ab\ne 0,a\ne (5b)/(3b-1)

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3x+1=((5x+2))/a+((x-1))/b

3 x + 1 = \frac{( 5 x + 2 )}{a} + \frac{( x - 1 )}{b}

x = \frac{2 b - a - ab}{3 ab - 5 b - a}; ab \neq = 0, a \neq = \frac{5 b}{3 b - 1}

Solution steps

3 x + 1 = \frac{( 5 x + 2 )}{a} + \frac{( x - 1 )}{b}

3 x + 1 = \frac{5 x + 2}{a} + \frac{x - 1}{b}

Multiply by LCM

3 x ab + ab = b (5 x + 2) + a (x - 1); ab \neq = 0

Expand

b (5 x + 2) : 5 b x + 2 b

3 x ab + ab = 5 b x + 2 b + a (x - 1)

Expand

a (x - 1) : a x - a

3 x ab + ab = 5 b x + 2 b + a x - a; ab \neq = 0

Move

ab

to the right side

3 x ab = 5 b x + 2 b + a x - a - ab; ab \neq = 0

Subtract

5 b x + a x

from both sides

3 x ab - (5 b x + a x) = 5 b x + 2 b + a x - a - ab - (5 b x + a x); ab \neq = 0

Simplify

3 ab x - 5 b x - a x = 2 b - a - ab; ab \neq = 0

Factor

3 ab x - 5 b x - a x : x (3 ab - 5 b - a)

x (3 ab - 5 b - a) = 2 b - a - ab; ab \neq = 0

Divide both sides by

3 ab - 5 b - a; ab \neq = 0, a \neq = \frac{5 b}{3 b - 1}

x = \frac{2 b - a - ab}{3 ab - 5 b - a}; ab \neq = 0, a \neq = \frac{5 b}{3 b - 1}

x^{2} - x - 20 = (x + a) (x - b)

x, 2 x + 6 y = 40

x, 2 x + 6 y = 21

3 (u + 5) = 33

13 (1 - x) = 78

What is the answer to 3x+1=((5x+2))/a+((x-1))/b ?
The answer to 3x+1=((5x+2))/a+((x-1))/b is x=(2b-a-ab)/(3ab-5b-a);\quad ab\ne 0,a\ne (5b)/(3b-1)