Rational Equations

Step 1: Find the least common denominator
The given equation is: To solve this, we first find the least common denominator (LCD) of the left-hand side. The LCD is .
Step 2: Rewrite the equation with the LCD
Multiply both terms on the left-hand side by and respectively: This simplifies to:
Step 3: Cross-multiply to solve for
Now, cross-multiply to eliminate the fractions:
Step 4: Expand both sides
Expand both sides of the equation:
Step 5: Rearrange the terms
Move all terms to one side of the equation:
Step 6: Solve the quadratic equation
We need to solve the quadratic equation . We can either factor or use the quadratic formula. Let's use the quadratic formula: For , , , and .
Answer:
Therefore, the solution to the equation is approximately . So, the correct answer is option (3).

These are parametric equations that represent a set of curves in the coordinate plane. The variable is a parameter that dictates the values of both and . By adjusting , the curves can be traced out.
- The equation represents the -coordinate in terms of .
- The equation represents the -coordinate in terms of .