Question
Solving Rational Equations Quick Check
3 of 53 of 5 Items
Question
What is the least common denominator of the equation 5x+5−1x2+2x−15=4x2+2x−15?(1 point)
Responses
(x+5)(x2+2x−15)
left parenthesis x plus 5 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis
(x+5)(x2+2x−15)(x2+2x−15)
left parenthesis x plus 5 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis left parenthesis x squared plus 2 x minus 15 right parenthesis
(x+5)
left parenthesis x plus 5 right parenthesis
(x+5)(x−3)
Answers
GPT-4o mini
To find the least common denominator (LCD) of the given rational equation, we need to first factor all the denominators present in the equation.
1. **Identify the denominators** in the equation:
- On the left side, there is a term \( -1/(x^2 + 2x - 15) \).
- On the right side, there is a term \( 4/(x^2 + 2x - 15) \).
2. **Factor the polynomial \( x^2 + 2x - 15 \)**:
\[
x^2 + 2x - 15 = (x + 5)(x - 3)
\]
3. **Identify all the factors:**
- The left side has a denominator of \( (x + 5)(x - 3) \).
- The right side also has the same denominator.
Since both sides of the equation share the same denominator \( (x + 5)(x - 3) \), the least common denominator for the equation will be:
\[
\text{LCD} = (x + 5)(x - 3)
\]
None of the options provided directly match this, but based on the options:
- **Correct Option:** \((x+5)(x−3)\)
So, the answer is:
**(x + 5)(x - 3)**
1. **Identify the denominators** in the equation:
- On the left side, there is a term \( -1/(x^2 + 2x - 15) \).
- On the right side, there is a term \( 4/(x^2 + 2x - 15) \).
2. **Factor the polynomial \( x^2 + 2x - 15 \)**:
\[
x^2 + 2x - 15 = (x + 5)(x - 3)
\]
3. **Identify all the factors:**
- The left side has a denominator of \( (x + 5)(x - 3) \).
- The right side also has the same denominator.
Since both sides of the equation share the same denominator \( (x + 5)(x - 3) \), the least common denominator for the equation will be:
\[
\text{LCD} = (x + 5)(x - 3)
\]
None of the options provided directly match this, but based on the options:
- **Correct Option:** \((x+5)(x−3)\)
So, the answer is:
**(x + 5)(x - 3)**