What is the answer to ((3x+7))/((x+2)+x)= 1/((x+2)+8) ?

The answer to ((3x+7))/((x+2)+x)= 1/((x+2)+8) is x=(-35+sqrt(409))/6 ,x=(-35-sqrt(409))/6

Solve for x: ((3x+7))/((x+2)+x)= 1/((x+2)+8)

The solution is x=(-35+sqrt(409))/6 ,x=(-35-sqrt(409))/6

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\frac{( 3 x + 7 )}{( x + 2 ) + x} = \frac{1}{( x + 2 ) + 8}

x = \frac{- 35 + 409}{6}, x = \frac{- 35 - 409}{6}

Decimal Notation

x = - 2.46270 \dots, x = - 9.20395 \dots

Solution steps

\frac{( 3 x + 7 )}{( x + 2 ) + x} = \frac{1}{( x + 2 ) + 8}

Cross multiply

(3 x + 7) (x + 10) = 2 x + 2

Solve

(3 x + 7) (x + 10) = 2 x + 2 : x = \frac{- 35 + 409}{6}, x = \frac{- 35 - 409}{6}

x = \frac{- 35 + 409}{6}, x = \frac{- 35 - 409}{6}

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = - 10

Combine undefined points with solutions:

x = \frac{- 35 + 409}{6}, x = \frac{- 35 - 409}{6}

\frac{( x + 1 )}{3} = \frac{21}{2 + 2 x - 1}

a, (a + b)^{- 1} = a^{- 1} + b^{- 1}

\frac{4}{x ^{2}} = \frac{1}{( a - x ) 2}

\frac{12}{23} = \frac{0.5}{x}

u, \frac{1}{u} + \frac{1}{v} = \frac{1}{f}

What is the answer to ((3x+7))/((x+2)+x)= 1/((x+2)+8) ?
The answer to ((3x+7))/((x+2)+x)= 1/((x+2)+8) is x=(-35+sqrt(409))/6 ,x=(-35-sqrt(409))/6
Solve for x: ((3x+7))/((x+2)+x)= 1/((x+2)+8)
The solution is x=(-35+sqrt(409))/6 ,x=(-35-sqrt(409))/6