Question

Is it true that (x^2-3x+2)/(x-1) = x – 2, for all values of x? Justify your answer.

Answer 1

Yes, it is true for all values of x.

Explanation:

We have given the equation:

(x²-3x+2)/(x-1) = x-2

First we solve the nominator L.H.S by factorization method.

x²-3x+2=0

x²-x-2x+2=0

x( x-1)-2( x-1)= 0

(x-1)(x-2)=0

Putting the value of nominator of L.H.S in the equation we get,

(x-1)(x-2)/(x-1)= (x-2)

Simplifying it we get,

(x-2) = (x-2)

Hence, L.H.S = R.H.S

So, it is true for all values of x.

Answer 2

It is true for all values of x

Explanation:

`((x^2-3x + 2))/(x-1) = x - 2`

`((x^2-3x + 2))/(x-1) = x-2`

First lets simplify Left hand side

LHS =
`((x^2-3x + 2))/(x-1)`

Solving the numerator of LHS

x² - 2x - x +2

Using factorization to simplify

x(x-2) - 1(x-2)

(x-1)(x-2)

LHS becomes

`((x-1)(x-2))/(x-1)`

(x-1) will cancel out

LHS = (x-2)

LHS = RHS

x-2 = x-2

It is evident from the above expression that
`((x^2-3x + 2))/(x-1) = x - 2` is true for all values of x