Question

Solve
the equation (x+1/x-1)+(x+2/x-2)= 2x+13/x+1​

Answer 1

Step-by-step explanation:

hope this helps buddy !!!

Answer 2

Answer:

The value of x can be $\frac{6}{5}$ or 5.

Step-by-step explanation:

GIVEN:  $\frac{x+1}{x-1} +\frac{x+2}{x-2} =\frac{2x+13}{x+1}$

SOLUTION:

To solve the given equation ,we will first simplify left hand side and right hand side separately.

First we will simplify left hand side,

$\frac{x+1}{x-1} +\frac{x+2}{x-2}$

By making the common denominator of the equation, we get

⇒$\frac{(x+1)(x-2)+(x+2)(x-1)}{(x-1)(x-2)}$

By multiplying and opening the brackets of the numerator

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

By further solving and simplifying the equations on the numerator,

⇒$\frac{2x^{2}-4 }{(x-1)(x-2)}$

Now solving both left hand side and right hand side together,

$\frac{2x^{2}-4 }{(x-1)(x-2)} =\frac{2x+13}{x+1}$

By multiplying denominator of left hand side to numerator of right hand side and by multiplying denominator of right hand side to numerator of left hand side, we get

$(2x^{2}-4)(x+1)=(2x+13)(x-1)(x-2)$

By solving the equation and opening the brackets,

$2x^{3}+2x^{2} -4x-4=(2x+13)(x^{2} -2x-x+2)$

$2x^{3}+2x^{2} -4x-4=(2x+13)(x^{2} -3x+2)$

$2x^{3}+2x^{2} -4x-4=2x^{3} -6x^{2} +4x+13x^{2} -39x+26$

Now simplifying the expressions on both sides,

$2x^{3}+2x^{2} -4x-4=2x^{3} +7x^{2} -35x+26$

further solving the equation, we get

$5x^{2} -31x+30=0$

Now solving the quadratic equation,

$5x^{2} -25x-6x+30=0$

$5x(x-5)-6(x-5)=0$

$(5x-6)(x-5)=0$

So here two possible solution are there . They are

$5x-6=0$ and $x-5=0$

From the above equations there are two value of x is possible. They are

$x=\frac{6}{5}$ and x=5

To solve similar quadratic questions,

https://brainly.in/question/2611921

https://brainly.in/textbook-solutions/q-value-5-1-2-x-3

Thank you