What is the answer to ((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36) ?

The answer to ((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36) is x=4

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((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36)

\frac{( 4 x + 17 )}{18} - \frac{( 13 x - 2 )}{( 17 x - 32 )} + \frac{x}{3} = \frac{( 7 x )}{12} - \frac{( x + 16 )}{36}

x = 4

Solution steps

\frac{( 4 x + 17 )}{18} - \frac{( 13 x - 2 )}{( 17 x - 32 )} + \frac{x}{3} = \frac{( 7 x )}{12} - \frac{( x + 16 )}{36}

Multiply by LCM

340 x^{2} - 530 x - 1016 = 340 x^{2} - 912 x + 512

Move

1016

to the right side

340 x^{2} - 530 x = 340 x^{2} - 912 x + 1528

Subtract

340 x^{2} - 912 x

from both sides

340 x^{2} - 530 x - (340 x^{2} - 912 x) = 340 x^{2} - 912 x + 1528 - (340 x^{2} - 912 x)

Simplify

382 x = 1528

Divide both sides by

382

x = 4

Verify Solutions

Find undefined (singularity) points:

x = \frac{32}{17}

Combine undefined points with solutions:

x = 4

\frac{1}{2 ( x + 5 ) ^{2} + 2} = 42.5

x^{- 3} = 2

x, \frac{y}{x} = 5

x (1 - x) = \frac{1}{( x ^{2} + 1 )}

\frac{( x ^{2} + x )}{x} = 1

What is the answer to ((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36) ?
The answer to ((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36) is x=4
Solve for x: ((4x+17))/(18)-((13x-2))/((17x-32))+x/3 =((7x))/(12)-((x+16))/(36)
The solution is x=4