QuestionSolving Rational Equations Solve each of the following rational equations algebraically (also called symbolically). Check your work by plugging the value(s) back into the equation or by graphing. Note: You must give each answer as an integer or reduced fraction and written as an equation.
Studdy Solution
STEP 1
1. Each equation involves rational expressions that need to be solved for .
2. Solutions should be verified by substituting back into the original equation or by graphing.
3. Answers should be presented as integers or reduced fractions.
STEP 2
1. Solve the equation .
2. Solve the equation .
3. Solve the equation .
4. Solve the equation .
STEP 3
For the equation , multiply both sides by to eliminate the fraction:
Expand and simplify:
Add 16 to both sides:
Divide by 8:
STEP 4
For the equation , cross-multiply to eliminate the fractions:
Expand both sides:
Rearrange terms to isolate :
Divide by -2:
STEP 5
For the equation , cross-multiply to eliminate the fractions:
Expand both sides:
Rearrange terms to isolate :
Divide by 4:
STEP 6
For the equation , first subtract 2 from both sides:
Multiply both sides by to eliminate the fraction:
Expand and simplify:
Subtract 48 from both sides:
Divide by 8:
The solutions are:
1.
2.
3.
4.
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