QuestionSolve the equation. Check the solutions.
Studdy Solution
STEP 1
1. The equation involves rational expressions.
2. We need to find a common denominator to combine the fractions.
3. We will solve for and check if the solutions are valid.
STEP 2
1. Find a common denominator and combine the fractions.
2. Solve the resulting equation for .
3. Check the solutions for validity.
STEP 3
First, identify the denominators in the equation: and . The common denominator will be the product of these two, which is .
STEP 4
Rewrite each term with the common denominator:
Combine the fractions on the left side:
Now, set the equation equal to the right side:
STEP 5
Cross-multiply to eliminate the fractions:
Expand both sides:
STEP 6
Rearrange the equation to form a quadratic equation:
STEP 7
Solve the quadratic equation using the quadratic formula:
The quadratic formula is:
For our equation, , , and .
Calculate the discriminant:
Calculate the roots:
This gives two solutions:
STEP 8
Check the solutions to ensure they do not make any denominator zero and satisfy the original equation.
For :
For :
Check if :
Substitute back into the original equation and verify:
Both solutions are valid.
The solutions are:
Was this helpful?