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Question
Solve the following equation:
`(3"x")/("x" + 6) - "x"/("x" + 5) = 2`
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Solution
`(3"x")/("x" + 6) - "x"/("x" + 5) = 2`
⇒ `(3"x"("x" + 5) - "x"("x" + 6))/(("x" + 6)("x" + 5)) = 2`
⇒ `(3"x"^2 + 15"x" - "x"^2 - 6"x")/("x"^2 + "5x" + "6x" + 30) = 2`
⇒ `(2"x"^2 + 9"x")/("x"^2 + 11"x" + 30) = 2`
⇒ 2x2 + 9x = 2 (x2 + 11x + 30)
⇒ 2x2 + 9x = 2x2 + 22x + 60
⇒ 2x2 - 2x2 + 9x - 22x = 60
⇒ -13 x = 60
x = `-60/13 = -4 8/13`
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