Math, asked by sumit9xm, 1 year ago

solve for x, x-1/2x+1 + 2x+1/x-1 =2 , where does not = -1/2,1

Answers

Answered by A1111
3
The difference of numerators and denominators of the terms on L.H.S. :-

2x + 1 - x + 1 = x + 2

Similarly,2x + 1 - x + 1 = x +2

For this, the difference should be equal or proportional and here as we see the difference is equal.

Thus by putting one of the difference equals to zero, we can find the value of the variable.

Hence, x + 2 = 0
=> x = -2

This is a quadratic equation. So, there will be two roots, where each is -2

These types methods are only for fast solving.

Hope this will help you and you will use it....

sumit9xm: please i want full answer..
A1111: In such cases just split the sign of R.H.S.
sumit9xm: okay thanks.
A1111: But, for this you have to learn sime Vedic rules or conditions
A1111: So wait, I will solve it
sumit9xm: ☺️ok..
Answered by siddhartharao77
3
 Given: \frac{x - 1}{2x + 1} + \frac{2x + 1}{x - 1} = 2

On cross-multiplication, we get

 \frac{(x - 1) * (x - 1)+ (2x + 1)(2x + 1)}{(x - 1)(2x + 1)} = 2

 \frac{(x - 1)^2 + (2x + 1)^2}{(x - 1)(2x + 1)} = 2

We know that (a - b)^2 = a^2 + b^2 - 2ab, (a + b)^2 = a^2 + b^2 + 2ab

 \frac{(x^2 + 1 - 2x) + (4x^2 + 1 + 4x)}{(x - 1)(2x + 1)} = 2

x^2 + 1 - 2x + 4x^2 + 1 + 4x = 2(x - 1)(2x + 1)

5x^2 + 2x + 2 = 2(2x^2 + x - 2x - 1)

5x^2 + 2x + 2 = 4x^2 + 2x - 4x - 2

5x^2 + 2x + 2 = 4x^2 - 2x - 2

x^2 + 4x + 4 = 0

(x + 2)^2 = 0

x = -2.


Therefore the value of x = -2.


Hope this helps!

sumit9xm: thanks brother
siddhartharao77: :-))
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