X + 1 upon x minus 1 plus x minus 2 upon X + 2 is equal to 4 minus 2 X + 3 upon X - 2
Answers
Answer:
I hope you understand well.
Step-by-step explanation:
Given,
(x+1)/(x-1) + (x-2)/(x+2) = 4 - (2x+3)/(x-2)
To find,
The value of x.
Solution,
The values of x will be -5 or 6/5.
We can easily solve this problem by following the given steps.
According to the question,
(x+1)/(x-1) + (x-2)/(x+2) = 4 - (2x+3)/(x-2)
Taking the LCM of the denominators on the left-hand side and right-hand side,
{(x+1)(x+2)+(x-2)(x-1)}/(x-1)(x+2) = {4(x-2)-(2x+3)}/(x-2)
(x²+2x+x+2+x²-x-2x+2)/(x-1)(x-2)= (4x-8-2x-3)/(x+2)
(2x²)/(x-1)(x+2) = (2x-11)/(x-2)
(2x²+4)/(x²+2x-x-2) = (2x-11)/(x-2)
Using the cross multiplication method,
(2x²+4) (x-2) = (x²+x-2)(2x-11)
(2x³-4x²+4x-8) = 2x³-11x²+2x²-11x-4x+22
2x³-4x²+4x-8 = 2x³-9x²-15x+22
Moving all the terms from the right-hand side to the left-hand side will result in the change of their from plus to minus or minus to plus,
2x³-2x³+9x²-4x²+15x+4x-8-22 = 0
5x²+19x-30 = 0
Now, factorising this expression by splitting the middle term such that their subtraction will be 19x and multiplication will be (-30×5),
5x²+25x-6x-30 = 0
Taking 5x common from the first two terms and -6 common from the last two terms,
5x(x+5)-6(x+5) = 0
(x+5)(5x-6) = 0
(x+5) = 0 or (5x-6) = 0
x = -5 or x = 6/5
Hence, the values of x are -5 or 6/5.