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Question
Solve the following equation by using formula :
`(4)/(3) - 3 = (5)/(2x + 3), x ≠ 0, -(3)/(2)`
Solution
`(4)/(3) - 3 = (5)/(2x + 3), x ≠ 0, -(3)/(2)`
⇒ `(4 - 3x)/x = (5)/(2x + 3)`
⇒ (4 – 3x)(2x + 3) = 5x
⇒ 8x + 12 – 6x2 – 9x – 5x = 0
⇒ –6x2 – 6x + 12 = 0
⇒ x2 + x – 2 = 0
⇒ x2 + 2x – x – 2 = 0
⇒ x(x + 2) –1(x + 2) = 0
⇒ (x + 2)(x – 1) = 0
Either x + 2 = 0,
then x = –2
or
x – 1 = 0,
then x = 1
∴ x = 1, –2.
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