Question

1/(x-1) +2/(x-2)=3/(x-3)​

Answer 1

Answer:

(x−1)(x−2)(x−3)

x−3+x−1

​

=

3

2

​

x

3

−6x

2

+11x−6

2x−4

​

=

3

2

​

x

3

−6x

2

+11x−6

2(x−2)

​

=

3

2

​

x

3

−6x

2

+11x−6

x−2

​

=

3

1

​

3x−6=x

3

−6x

2

+11x−6

x

3

−6x

2

+8x=0

x(x

2

−6x+8)=0

x

2

−6x+8=0

​

Now, solve this equation, to get the value of x ;

\begin{gathered}\mathsf{x {}^{2} - 6x + 8 = 0} \\ \\ \mathsf{x {}^{2} - 4x - 2x + 8 = 0 } \\ \\ \mathsf{x(x - 4) - 2(x - 4) = 0} \\ \\ \mathsf{(x - 2)(x - 4) = 0}\end{gathered}

x

2

−6x+8=0

x

2

−4x−2x+8=0

x(x−4)−2(x−4)=0

(x−2)(x−4)=0

​

Hence,

\begin{gathered}\mathsf{(x - 2) = 0} \\ \\ \therefore\mathsf{x = 2}\end{gathered}

(x−2)=0

∴x=2

​

And,

\begin{gathered}\mathsf{(x - 4) = 1} \\ \\ \therefore \mathsf{x = 4}\end{gathered}

(x−4)=1

∴x=4

​

Step-by-step explanation: