Question

(3/x-2)-(2/x-3)=(4/x-3)-(3/x-1)​

Answer 1

Step-by-step explanation:

Given,

\dfrac{3}{x-2}-\dfrac{2}{x-3}=\dfrac{4}{x-3}-\dfrac{3}{x-1}

x−2

3

−

x−3

2

=

x−3

4

−

x−1

3

To find,

The value of x.

Solution,

We have,

\dfrac{3}{x - 2} - \dfrac{2}{x - 3} = \dfrac{4}{x - 3} - \dfrac{3}{x - 1}

x−2

3

−

x−3

2

=

x−3

4

−

x−1

3

Taking LCM on both the sides, we get :

\begin{gathered}\dfrac{3(x - 3) - 2(x - 2)}{(x - 2)(x - 3)} = \dfrac{4(x - 1) - 3(x - 3)}{(x - 3)(x - 1)} \\\\ \dfrac{3x - 9 - 2x + 4}{(x - 2)(x - 3)} = \dfrac{4x - 4 - 3x + 9}{(x - 3)(x - 1)}\end{gathered}

(x−2)(x−3)

3(x−3)−2(x−2)

=

(x−3)(x−1)

4(x−1)−3(x−3)

(x−2)(x−3)

3x−9−2x+4

=

(x−3)(x−1)

4x−4−3x+9

Now, solving both sides such that,

\begin{gathered}( x- 3)(x - 1)(x - 5) = (x + 5)(x - 2)(x - 3) \\\\( x - 1)(x - 5) = (x + 5)(x - 2) \\\\ {x}^{2} - 5x - x + 5 = {x}^{2} - 2x + 5x - 10 \\\\ {x}^{2} - 6x + 5 = {x}^{2} + 3x - 10 \\\\ {x}^{2} - {x}^{2} - 6x - 3x = - 10 - 5 \\\\ - 9x = -15\\\\x=\dfrac{5}{3}\end{gathered}

(x−3)(x−1)(x−5)=(x+5)(x−2)(x−3)

(x−1)(x−5)=(x+5)(x−2)

x

2

−5x−x+5=x

2

−2x+5x−10

x

2

−6x+5=x

2

+3x−10

x

2

−x

2

−6x−3x=−10−5

−9x=−15

x=

3

5

So, the value of x is 5/3.

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