Solve the Rational Equation 3/x + 2 = 2/(5x) + 21/10 College Algebra MyMathlab Homework

TL;DR

Identify restrictions, eliminate fractions, and solve for x in fractional equations.

Transcript

so in this question we're given an equation 3x plus 2 equals 2 over 5x plus 21 over 10 and Part A is asking us to figure out what makes the denominator 0 in other words what makes this equation not make any sense at all so you're not allowed to have 0 on the bottom well if you look maybe at just this first piece here you see you have an X in the bo... Read More

Key Insights

• ➗ Identifying restrictions in fractional equations prevents division by zero errors.
• ✖️ Multiplying by the least common multiple helps simplify equations with fractions.
• ☺️ Isolating x by step-by-step simplification leads to finding the solution.
• ⚾ Solutions to fractional equations may result in a specific value or no solution based on constraints.
• ❓ Understanding the logic behind restricting certain values in equations enhances problem-solving skills.
• ✖️ Multiplying by the least common multiple efficiently removes fractions for easier calculation.
• ❓ Step-by-step simplification of equations with fractions is crucial in obtaining accurate solutions.

Questions & Answers

Q: How do you identify restrictions in fractional equations?

Restrictions are found by determining what makes the denominator 0. Any value that would result in a 0 denominator is not allowed in the solution, as division by zero is undefined.

Q: How do you eliminate fractions in equations with x in the denominator?

To eliminate fractions with x in the denominator, multiply by x to cancel it out. This step ensures that the equation can be solved without fractions complicating the process.

Q: What steps are involved in solving fractional equations once the restrictions are identified?

After identifying restrictions, the next step is to multiply the equation by the least common multiple of the denominators to eliminate fractions. Then simplify the equation and isolate x to find the solution.

Q: What is the final step in solving a fractional equation and obtaining the value of x?

The final step involves simplifying the equation after eliminating fractions and isolating x. By solving for x, the final answer is obtained, which may be a specific value or no solution depending on the constraints.

Summary & Key Takeaways

• Identify restrictions by finding what makes the denominator 0 in the equation.

• Eliminate fractions by multiplying by the least common multiple of the denominators.

• Solve for x by simplifying the equation and isolating x.