Question

What is the least common denominator of the equation 5x+5−1x2+2x−15=4x2+2x−15 ?(1 point)%0D%0AResponses%0D%0A%0D%0A(x+5)(x−3)%0D%0Aleft parenthesis x plus 5 right parenthesis left parenthesis x minus 3 right parenthesis%0D%0A%0D%0A(x+5)%0D%0Aleft parenthesis x plus 5 right parenthesis%0D%0A%0D%0A(x+5)(x2+2x−15)%0D%0Aleft parenthesis x plus 5 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis%0D%0A%0D%0A(x+5)(x2+2x−15)(x2+2x−15)

Answer 1

To find the least common denominator (LCD) of the equation given, let's start by examining the denominators involved in the equation:

The equation is:
\[
\frac{5x + 5}{x^2 + 2x - 15} = \frac{4x^2 + 2x - 15}{1}
\]

The only denominator present is \(x^2 + 2x - 15\).

To factor \(x^2 + 2x - 15\):
1. We need to find two numbers that multiply to \(-15\) (the constant term) and add to \(2\) (the coefficient of \(x\)).
2. The numbers \(5\) and \(-3\) satisfy these conditions since \(5 \times -3 = -15\) and \(5 + (-3) = 2\).

Thus, we can factor:
\[
x^2 + 2x - 15 = (x + 5)(x - 3)
\]

So, the least common denominator (LCD) for the equation is:
\[
(x + 5)(x - 3)
\]

Now, reviewing the response options you provided:
1. \((x + 5)(x - 3)\)
2. \((x + 5)\)
3. \((x + 5)(x^2 + 2x - 15)\)
4. \((x + 5)(x^2 + 2x - 15)(x^2 + 2x - 15)\)

The correct choice is:
\[
\text{(x + 5)(x - 3)}
\]