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

The answer to 2/(x+3)+(x+3)/2 = 10/3 is x=3,x=-7/3

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2/(x+3)+(x+3)/2 = 10/3

\frac{2}{x + 3} + \frac{x + 3}{2} = \frac{10}{3}

x = 3, x = - \frac{7}{3}

Decimal

x = 3, x = - 2.33333 \dots

Solution steps

\frac{2}{x + 3} + \frac{x + 3}{2} = \frac{10}{3}

Multiply by LCM

12 + 3 (x + 3)^{2} = 20 (x + 3)

Solve

12 + 3 (x + 3)^{2} = 20 (x + 3) : x = 3, x = - \frac{7}{3}

x = 3, x = - \frac{7}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 3

Combine undefined points with solutions:

x = 3, x = - \frac{7}{3}

x - \frac{x + 5}{x + 8} = \frac{3}{x + 8}

\frac{20}{x} - \frac{20}{x - 2} = \frac{4}{x}

\frac{2}{x} - \frac{3 x}{2} = 7

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

2 x - \frac{32}{x} = 0

What is the answer to 2/(x+3)+(x+3)/2 = 10/3 ?
The answer to 2/(x+3)+(x+3)/2 = 10/3 is x=3,x=-7/3
Solve for x: 2/(x+3)+(x+3)/2 = 10/3
The solution is x=3,x=-7/3