What is the answer to 4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8 ?

The answer to 4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8 is x= 1/3 ,x=-9/5

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4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8

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

x = \frac{1}{3}, x = - \frac{9}{5}

Decimal Notation

x = 0.33333 \dots, x = - 1.8

Solution steps

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

Remove square roots

\frac{- 847 x ^{4} + 1156 x ^{3} + 3654 x ^{2} + 1476 x + 81}{x ^{4} + 2 x ^{3} + x ^{2}} + 4096 = \frac{2304 ( x + 1 )}{x}

Solve

\frac{- 847 x ^{4} + 1156 x ^{3} + 3654 x ^{2} + 1476 x + 81}{x ^{4} + 2 x ^{3} + x ^{2}} + 4096 = \frac{2304 ( x + 1 )}{x} : x = \frac{1}{3}, x = - \frac{9}{5}, x = \frac{- 35 + 16 7}{63}, x = - \frac{35 + 16 7}{63}

x = \frac{1}{3}, x = - \frac{9}{5}, x = \frac{- 35 + 16 7}{63}, x = - \frac{35 + 16 7}{63}

Verify Solutions:

x = \frac{1}{3}

True

, x = - \frac{9}{5}

True

, x = \frac{- 35 + 16 7}{63}

False

, x = - \frac{35 + 16 7}{63}

False

The solutions are

x = \frac{1}{3}, x = - \frac{9}{5}

\frac{x}{8} = \frac{x}{18}

64 (x) (64) = 32 \cdot 32

x^{2} + x + 1 = 1

m = \frac{m ^{0}}{1 - \frac{v ^{2}}{c ^{2}}}

x = \frac{2}{3}

What is the answer to 4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8 ?
The answer to 4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8 is x= 1/3 ,x=-9/5
Solve for x: 4sqrt(x/((x+1)))+3sqrt(((x+1))/x)=8
The solution is x= 1/3 ,x=-9/5