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प्रश्न
Solve the following equation by using formula :
`(2)/(x + 2) - (1)/(x + 1) = (4)/(x + 4) - (3)/(x + 3)`
उत्तर
`(2)/(x + 2) - (1)/(x + 1) = (4)/(x + 4) - (3)/(x + 3)`
`(2x + 2 - x - 2)/((x + 2)(x + 1)) = (4x + 12 - 3x - 12)/((x + 4)(x + 3)`
⇒ `x/((x + 2)(x + 1)) = x/((x + 4)(x + 3)`
⇒ `(1)/((x + 2)(x + 1)) = (1)/((x + 4)(x + 3)` ...[Dividing by x if x ≠ 0]
⇒ `(1)/(x^2 + 3x + 2) = (1)/(x^2 + 7x + 12)`
⇒ x2 + 7x + 12 – x2 – 3x – 2 = 0
⇒ 4x + 10
⇒ 2x + 5 = 0
⇒ 2x = –5
⇒ x = `(-5)/(2)`
If x = 0, then
`(0)/((x + 2)(x + 1)) = (0)/((x + 4)(x + 3)`
Which is correct
Hence x = 0, `(-5)/(2)`.
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