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WINSTONCH [101]
3 years ago
12

Answer to solving equation

Mathematics
1 answer:
Rufina [12.5K]3 years ago
7 0

Answer:

<h3>x = 5 or x = (-1)</h3>

Step-by-step explanation:

\frac{x}{x + 1}  -  \frac{2}{x - 2}  =  \frac{3}{ {x}^{2} - x - 2 }  \\  \frac{x(x - 2) - 2(x + 1)}{(x + 1)(x - 2)}  =  \frac{3}{ {x}^{2} - x - 2 }  \\  \frac{ {x}^{2}  - 2x - 2x - 2}{x(x - 2) + 1(x - 2)}  =  \frac{3}{ {x}^{2}  - x - 2}  \\  \frac{ {x}^{2} - 4x - 2 }{ {x}^{2}  - 2x + x - 2}  =  \frac{3}{ {x}^{2} - x - 2 }  \\  \frac{ {x}^{2} - 4x - 2 }{ {x}^{2} - x - 2 }  =  \frac{3}{ {x}^{2}  - x - 2}  \\ ( {x}^{2}  - 4x - 2)( {x}^{2}  - x - 2) = 3( {x}^{2}  - x - 2) \\  {x}^{2}  - 4x - 2 = 3 \\  {x}^{2}  - 4x - 2 - 3 = 0 \\  {x}^{2}  - 4x  - 5= 0 \\  {x}^{2}  + x - 5x - 5 = 0 \\ x(x +1 ) - 5(x + 1) = 0 \\ (x - 5)(x + 1) = 0 \\

(x - 5) = 0 or (x + 1) = 0 should be.

x = 5 or x = -1

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