Solve for x in the equation with fractions.

Published on October 24, 2024

Algebra

The solution for x in the equation involving fractions with (x-1) and (x+1) in the denominator is x = √2 and x = -√2.

Question

Answer

Let’s solve for x step-by-step:

Find a common denominator on the left side:

The common denominator for (x-1) and (x+1) is (x-1)(x+1). So we get:
Simplify the left side:

Expanding the numerator:

Combining like terms:
Notice that (x^2 - 1) factors:

The denominator on both sides can be factored:
Since the denominators are the same, we can equate the numerators:
Solve for x:

Subtract 2 from both sides:

Divide both sides by 2:

Take the square root of both sides:

Therefore, the solutions are x = √2 and x = -√2.

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