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प्रश्न
Solve the following equation.
`[10x^2 + 15x + 63]/[5x^2 - 25x + 12] = (2x + 3)/( x -5)`
उत्तर
`[10x^2 + 15x + 63]/[5x^2 - 25x + 12] = (2x + 3)/( x -5)`
By Alternando,
⇒ `[10x^2 + 15x + 63]/(2x + 3) =[5x^2 - 25x + 12]/( x -5)`
Multiplying both sides by `1/(5x)`, we get
`[10x^2 + 15x + 63]/(10x^2 + 15x) =[5x^2 - 25x + 12]/( 5x^2 -25x)`
Using dividendo, we get
`[(10x^2 + 15x + 63) - (10x^2 + 15x)]/(10x^2 + 15x) =[(5x^2 - 25x + 12) - ( 5x^2 -25x)]/( 5x^2 -25x)`
⇒ `(63)/[10x^2 + 15x] = 12/[5x^2 - 25x]`
⇒ `(63)/{5x (2x + 3)} = 12/{5x(x - 5)}`
⇒ `(63)/(2x + 3) = 12/(x - 5)`
⇒ `63(x - 5) = 12(2x + 3)`
⇒ `63x - 315 = 24x + 36`
⇒ `63x - 24x = 315 + 36`
⇒ `39x = 351`
⇒ x = `351/39`
⇒ x = 9
Thus, the solution of the given equation is x = 9.
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