What is the answer to (4x)/(x+3)+3/(x-4)=5 ?

The answer to (4x)/(x+3)+3/(x-4)=5 is x=-4-sqrt(85),x=sqrt(85)-4

Solve for x: (4x)/(x+3)+3/(x-4)=5

The solution is x=-4-sqrt(85),x=sqrt(85)-4

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\frac{4 x}{x + 3} + \frac{3}{x - 4} = 5

x = - 4 - 85, x = 85 - 4

Decimal Notation

x = - 13.21954 \dots, x = 5.21954 \dots

Solution steps

\frac{4 x}{x + 3} + \frac{3}{x - 4} = 5

Multiply by LCM

4 x (x - 4) + 3 (x + 3) = 5 (x + 3) (x - 4)

Solve

4 x (x - 4) + 3 (x + 3) = 5 (x + 3) (x - 4) : x = - 4 - 85, x = 85 - 4

x = - 4 - 85, x = 85 - 4

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 4

Combine undefined points with solutions:

x = - 4 - 85, x = 85 - 4

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

\frac{4}{x} = \frac{- 2}{9}

\frac{1 - 2 x}{x} = 4

\frac{9}{x} = 3

\frac{1}{x + 3} + 4 = \frac{21}{x + 3}

What is the answer to (4x)/(x+3)+3/(x-4)=5 ?
The answer to (4x)/(x+3)+3/(x-4)=5 is x=-4-sqrt(85),x=sqrt(85)-4
Solve for x: (4x)/(x+3)+3/(x-4)=5
The solution is x=-4-sqrt(85),x=sqrt(85)-4