Question

(X-1/x+2)+(x-3/x-5) = 10/3

Answer 1

Answer:

x= $\frac{37 ± \sqrt{197} }{8}$

Step explanation:

the first easiest step is to find the LCM,

[(x-1)(x-5)+(x-3)(x+2)/(x+2)(x-5)=10/3

multiple using the distributive law,

(x^2 - 6x + 5 + x^2 - 5x +6)/(x^2 - 7x + 10) =10/3

and multiply both side by (x^2 - 7x + 10) and 3,

3(2x^2 - 11x +11) = 10(x^2 - 7x + 10)

6x^2 - 33x + 33 = 10x^2 - 70x + 100

70x - 33x = 10x^2 - 6x^2 + 100 - 33

on solving further we get,

37x = 4x^2 + 67

which is,

4x^2 - 37x + 67 = 0

and,

$\sqrt{d}$=$\sqrt{B^{2} - 4AC }$

hence,

$\sqrt{d}$= $\sqrt{37^{2}-(4)(4)(67)}$

$\sqrt{d}$=$\sqrt{197}$

now,

we know that ,

x = $\frac{- B ± \sqrt{d} }{(2)(A)}$

therefore,

x= $\frac{37 ± \sqrt{197} }{8}$

hence the value of x is found.