Math Problem Statement

2/x-3/x+1 /4/x+1+5/x

Solution

To simplify the expression 2x3x+1÷4x+1+5x\frac{2}{x} - \frac{3}{x + 1} \div \frac{4}{x + 1} + \frac{5}{x}, follow these steps:

Step 1: Simplify the division

The expression has a division: 3x+1÷4x+1\frac{3}{x + 1} \div \frac{4}{x + 1}. To simplify this:

3x+1÷4x+1=3x+1×x+14=34\frac{3}{x + 1} \div \frac{4}{x + 1} = \frac{3}{x + 1} \times \frac{x + 1}{4} = \frac{3}{4}

Step 2: Substitute back into the expression

Now, substitute 34\frac{3}{4} back into the original expression:

2x34+5x\frac{2}{x} - \frac{3}{4} + \frac{5}{x}

Step 3: Combine like terms

Combine the terms that have the common denominator xx:

2x+5x=2+5x=7x\frac{2}{x} + \frac{5}{x} = \frac{2 + 5}{x} = \frac{7}{x}

So, the simplified expression is:

7x34\frac{7}{x} - \frac{3}{4}

Final Answer:

The simplified form of the given expression is:

7x34\frac{7}{x} - \frac{3}{4}

Would you like more details on any of these steps?


Here are 5 related questions:

  1. How do you add or subtract fractions with different denominators?
  2. How do you simplify a complex fraction?
  3. What is the difference between multiplying and dividing fractions?
  4. How do you solve equations involving fractions?
  5. How can you simplify expressions with multiple fractions?

Tip: When dividing fractions, remember to multiply by the reciprocal of the divisor.

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Combining Fractions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9