x+2= 3
x=3-2
x=1
ago 3 yrs = 9 months
after 5 yrs=5yrs
Let Rehman's present age be 'x'.
So, Rehman's age 3 years ago would be 'x - 3'
And, Rehman's age 5 years later would be 'x + 5'
__________________________
According to the question,
[tex]\dfrac{1}{x - 3} + \dfrac{1}{x+5} = \dfrac{1}{3}[/tex]
Let's simplify.
⇒ [tex]\dfrac{1}{x - 3} + \dfrac{1}{x+5} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{x+5 + x - 3}{(x - 3)(x+5)} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x (x+5) - 3 (x +5)} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x^{2} + 5x - 3x - 15} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x^{2} + 2x - 15} = \dfrac{1}{3}[/tex]
Now, cross multiply.
⇒ 3 (2x + 2) = 1 (x² + 2x - 15)
⇒ 6x + 6 = x² + 2x - 15
Flip the equation and simplify further.
⇒ x² + 2x - 15 = 6x + 6
⇒ x² + 2x - 6x - 15 - 6 = 0
⇒ x² - 4x - 21 = 0
Now, find the zeroes of the obtained quadratic equation by the factorisation method.
⇒ x² - 7x + 3x - 21 = 0
⇒ x (x - 7) + 3 (x - 7) = 0
⇒ (x + 3) (x - 7) = 0
⇒ x = -3 or x = 7
∴ x = -3 (rejected, because age cannot be negative)
∴ x = 7
∴ Rehman's present age is 7 years.
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Answers & Comments
x+2= 3
x=3-2
x=1
ago 3 yrs = 9 months
after 5 yrs=5yrs
Let Rehman's present age be 'x'.
So, Rehman's age 3 years ago would be 'x - 3'
And, Rehman's age 5 years later would be 'x + 5'
__________________________
According to the question,
[tex]\dfrac{1}{x - 3} + \dfrac{1}{x+5} = \dfrac{1}{3}[/tex]
Let's simplify.
⇒ [tex]\dfrac{1}{x - 3} + \dfrac{1}{x+5} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{x+5 + x - 3}{(x - 3)(x+5)} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x (x+5) - 3 (x +5)} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x^{2} + 5x - 3x - 15} = \dfrac{1}{3}[/tex]
⇒ [tex]\dfrac{2x+ 2}{x^{2} + 2x - 15} = \dfrac{1}{3}[/tex]
__________________________
Now, cross multiply.
⇒ 3 (2x + 2) = 1 (x² + 2x - 15)
⇒ 6x + 6 = x² + 2x - 15
__________________________
Flip the equation and simplify further.
⇒ x² + 2x - 15 = 6x + 6
⇒ x² + 2x - 6x - 15 - 6 = 0
⇒ x² - 4x - 21 = 0
__________________________
Now, find the zeroes of the obtained quadratic equation by the factorisation method.
⇒ x² - 4x - 21 = 0
⇒ x² - 7x + 3x - 21 = 0
⇒ x (x - 7) + 3 (x - 7) = 0
⇒ (x + 3) (x - 7) = 0
⇒ x = -3 or x = 7
∴ x = -3 (rejected, because age cannot be negative)
∴ x = 7
∴ Rehman's present age is 7 years.
__________________________