What is the answer to ((x-3))/((x+3))-((x+3))/((x-3))= 48/7 ?

The answer to ((x-3))/((x+3))-((x+3))/((x-3))= 48/7 is x= 9/4 ,x=-4

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((x-3))/((x+3))-((x+3))/((x-3))= 48/7

\frac{( x - 3 )}{( x + 3 )} - \frac{( x + 3 )}{( x - 3 )} = \frac{48}{7}

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

Decimal Notation

x = 2.25, x = - 4

Solution steps

\frac{( x - 3 )}{( x + 3 )} - \frac{( x + 3 )}{( x - 3 )} = \frac{48}{7}

Multiply by LCM

7 (x - 3)^{2} - 7 (x + 3)^{2} = 48 (x + 3) (x - 3)

Solve

7 (x - 3)^{2} - 7 (x + 3)^{2} = 48 (x + 3) (x - 3) : x = \frac{9}{4}, x = - 4

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

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 3

Combine undefined points with solutions:

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

\frac{x + 2}{x - 2} = \frac{6}{10}

\frac{1}{a} = a^{- 1}

x^{2} + \frac{1}{x ^{2}} - 3 x - \frac{3}{x} + 4 = 0

a = - 10 m \cdot s^{- 2}

\frac{x ^{2} + 3 x - 20}{( x ^{2} + 3 x )} = 8

What is the answer to ((x-3))/((x+3))-((x+3))/((x-3))= 48/7 ?
The answer to ((x-3))/((x+3))-((x+3))/((x-3))= 48/7 is x= 9/4 ,x=-4
Solve for x: ((x-3))/((x+3))-((x+3))/((x-3))= 48/7
The solution is x= 9/4 ,x=-4