Question

solve for the equation
6/x -2 /x-1 =1/x-2
​

Answer 1

Step-by-step explanation:

Given :

6/x -2 /x-1 =1/x-2

To Find :

what is the value of x

Concept :

How To Find LCM ?

The least common multiple, or LCM, is another number that's useful in solving many math problems. Let's find the LCM of 30 and 45. One way to find the least common multiple of two numbers is to first list the prime factors of each number.

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2: one occurrence

3: two occurrences

5: one occurrence

2 × 3 × 3 × 5 = 90

After you've calculated a least common multiple, always check to be sure your answer can be divided evenly by both numbers.

How To Do Cross Multiplying ?

The method of cross-multiplying means that we multiply the numerator of each (or one) side by the denominator of the other side, effectively crossing the terms over.

Now Solution the Given Equation :

$\sf : \implies \: \: \: \: \: \: \: \: \: \frac{6}{x } - \frac{2}{x - 1} = \frac{1}{x - 2}$

We Find the LCM :

$\sf : \implies \: \: \: \: \: \: \: \: \: \frac{6}{x } - \frac{2}{x - 1} = \frac{1}{x - 2} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \frac{6(x - 1) - (2x)}{ {x}^{2} - x} = \frac{1}{x - 2} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: \: \: \frac{6x - 6 - 2x}{ {x}^{2} - x} = \frac{1}{x - 2}$

On Cross Multiplying :

$\: \sf : \implies \: \: \: \: \: \: \: \: \: {x}^{2} - x = \: {4x}^{2} - 14x + 12 \\ \\ \\ \: \sf : \implies \: \: \: \: \: \: \: \: {4x}^{2} - {x}^{2} - 14x + x + 12 \\ \\ \\ \: \sf : \implies \: \: \: \: \: \: \: \: {3x}^{2} - 13x + 12$

$\: \sf : \implies \: \: \: \: \: \: \: \: \: {3x}^{2} - 9x - 4x + 12 \\ \\ \\\: \sf : \implies \: \: \: \: \: \: \: \: \: 3x(x - 3) - 4( x- 3) \\ \\ \\ \: \sf : \implies \: \: \: \: \: \: \: \: \:(3x - 4)(x - 3)$

Hence the Value of x is 4/3 And 3

Answer 2

Answer:

The equation

x−2x−1=1−2x−1

doesn't have a solution. What this means is that there are no real numbers that satisfy the equation. That is, you can't find a number x such that

x−2x−1=1−2x−1

How can you see this. First note that x=1 is not a solution because you can't divide by zero. Note then that if you add 2/(x−1) to both sides of the equation, then x=1. So the only possible solution is x=1, but this doesn't work as we just figured out

Step-by-step explanation:

Hope it helps!+