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प्रश्न
Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x
Solve for x:
`14/(x+3)-1=5/(x+1)`
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उत्तर
`14/(x+3)-1=5/(x+1); xne-3,-1`
It can be rewritten as:
⇒ `(14 - (x - 3))/(x+3)-5/(x+1)`
`(14 - x -3)/(x + 3) = 5/(x + 1)`
`(11 - x)/(x + 3) = 5/(x + 1)`
⇒ (11 − x)(x + 1) = 5(x + 3)
⇒ 11x + 11 − x2 − x = 5x + 15
⇒ −x2 + 10x + 11 = 5x + 15
⇒ −x2 + 10x − 5x + 11 − 15 = 0
⇒ −x2 + 5x −4 = 0
⇒ x2 − 5x + 4 = 0
⇒ x2 − 4x − x + 4 = 0
⇒ x(x − 4) −1(x − 4) = 0
⇒ (x − 1)(x − 4) = 0
⇒ x = 1 or x = 4.
Thus, the solution of the given equation is 1 or 4.
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