Question

Solve by factorising:

$11. \: \frac{x}{x + 1} + \frac{x + 1}{x} = \frac{34}{15}$
x # - 1 , 0

From Quadratic Equation

Standard:- 10

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Answer 1

Hey!!!

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Difficulty Level : Above Average

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Note : I'm using my secret method, you may not get this method any where else !!

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We have

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{34}{15}$

Now here

Let

$\frac{x}{x + 1} = a$

It becomes

=> a + 1/a = 34/15

Easy ?

Let's solve this

=> (a² + 1)/a = 34/15

=> 15a² + 15 = 34a

=> 15a² - 34a + 15 = 0

Here , 15 x 15 = 225

=> 225 = 9 x 25

Thus by middle term splitting method

=> 15a² - 9a - 25a + 15 = 0

=> 3a(5a - 3) - 5(5a - 3) = 0

=> (3a - 5)(5a - 3) = 0

Thus we have

=> a = 5/3 or a = 3/5

Case 1, a = 5/3

=> x/(x + 1) = 5/3

=> 3x = 5x + 5

=> x = - 5/2 <<<<<< Answer

Case 2, a = 3/5

=> x/(x + 1) = 3/5

=> 5x = 3x + 3

=> 2x = 3

=> x = 3/2 <<<<<<<<< Answer

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Hope this method is clear

Good Night :-)

Answer 2

The solution is in the attachment.