What is the answer to (2z)/(z+3)= 3/(z-10)+2 ?

The answer to (2z)/(z+3)= 3/(z-10)+2 is z= 17/3

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(2z)/(z+3)= 3/(z-10)+2

\frac{2 z}{z + 3} = \frac{3}{z - 10} + 2

z = \frac{17}{3}

Decimal Notation

z = 5.66666 \dots

Solution steps

\frac{2 z}{z + 3} = \frac{3}{z - 10} + 2

Multiply by LCM

2 z^{2} - 20 z = 2 z^{2} - 11 z - 51

Subtract

2 z^{2} - 11 z

from both sides

2 z^{2} - 20 z - (2 z^{2} - 11 z) = 2 z^{2} - 11 z - 51 - (2 z^{2} - 11 z)

Simplify

- 9 z = - 51

Divide both sides by

- 9

z = \frac{17}{3}

Verify Solutions

Find undefined (singularity) points:

z = - 3, z = 10

Combine undefined points with solutions:

z = \frac{17}{3}

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

\frac{z ^{6} + 1}{z ^{2} + 1} = 0

a, z = b + \frac{m}{a}

\frac{1}{x} = \frac{6}{x ^{2}}

12 x - \frac{288}{x ^{2}} = 0

What is the answer to (2z)/(z+3)= 3/(z-10)+2 ?
The answer to (2z)/(z+3)= 3/(z-10)+2 is z= 17/3
Solve for z: (2z)/(z+3)= 3/(z-10)+2
The solution is z= 17/3