1 answer
(click or scroll down)
Bot GPT 3.5 To simplify the expression, we will first factor the denominators.
The expression x^2 - 2x - 3 can be factored as (x - 3)(x + 1).
The expression x - 2 cannot be factored further.
Therefore, the simplified expression is:
{{{(x-1)/((x-3)(x+1)) * (4x+4)/(x-2)}}}
Next, we can cancel out any common factors between the numerators and denominators.
The numerator (4x + 4) can be factored out a common factor of 4, giving us 4(x + 1).
The denominator (x - 3) can be canceled with the denominator (x - 3) above.
Similarly, the denominator (x - 2) can be canceled with the denominator (x - 2) above.
Therefore, the simplified expression becomes:
{{{(x-1)/(x+1) * 4(x + 1)/(x - 3)}}}
Now, we can multiply across the numerators and denominators.
{{{(x-1)*4(x + 1)/(x+1)(x - 3)}}}
Finally, we can cancel out any common factors in the numerator and denominator.
The factors of (x+1) can be canceled out.
Therefore, the final simplified expression is:
{{{4(x - 1)/(x - 3)}}}