Which Expression Is Equivalent To The Following Complex Fraction

Which Expression Is Equivalent To The Following Complex Fraction

In mathematics, a complex fraction is a fraction whose numerator or denominator is itself a fraction. For example, the expression

\frac{2}{x + 3} \div \frac{5}{y - 2} 

is a complex fraction. To simplify a complex fraction, we can use the following steps:

1. Simplify the numerator and denominator of each fraction independently.
2. Multiply the numerator and denominator of the resulting fraction by the product of the denominators of the original fractions.
3. Simplify the resulting fraction.

For example, to simplify the complex fraction above, we would first simplify the numerator and denominator of each fraction independently. The numerator of the first fraction can be simplified by combining like terms:

\frac{2}{x + 3} = \frac{2 - 2x}{x + 3} = \frac{-2x}{x + 3} 

The denominator of the second fraction can be simplified by combining like terms:

\frac{5}{y - 2} = \frac{5 - 10y}{y - 2} = \frac{-10y}{y - 2} 

Now that we have simplified the numerator and denominator of each fraction, we can multiply the numerator and denominator of the resulting fraction by the product of the denominators of the original fractions:

\frac{-2x}{x + 3} \div \frac{-10y}{y - 2} = \frac{-2x \cdot (y - 2)}{(x + 3) \cdot (-10y)} 

Finally, we can simplify the resulting fraction:

\frac{-2x \cdot (y – 2)}{(x + 3) \cdot (-10y)} = \frac{-2xy + 4x}{-10xy – 30x} = \frac{2xy – 4x}{10xy + 30x}

Therefore, the simplified form of the complex fraction is $\frac{2xy – 4x}{10xy + 30x}$.

Related Questions

Here are some related questions that can be asked about complex fractions:

• What is the difference between a simple fraction and a complex fraction?
• How do you simplify a complex fraction?
• What are some tips for simplifying complex fractions?

Answers

• A simple fraction is a fraction whose numerator and denominator are both integers. A complex fraction is a fraction whose numerator or denominator is itself a fraction.
• To simplify a complex fraction, we can use the following steps:
  1. Simplify the numerator and denominator of each fraction independently.
  2. Multiply the numerator and denominator of the resulting fraction by the product of the denominators of the original fractions.
  3. Simplify the resulting fraction.
• Here are some tips for simplifying complex fractions:
  • Start by simplifying the numerator and denominator of each fraction independently. This will often make the fraction easier to work with.
  • When multiplying the numerator and denominator of the resulting fraction, be careful to distribute any negative signs.
  • If the resulting fraction is still complicated, you can try to factor the numerator or denominator.

Here are some examples of how to answer these questions:

• What is the difference between a simple fraction and a complex fraction?

• Answer: A simple fraction is a fraction whose numerator and denominator are both integers. A complex fraction is a fraction whose numerator or denominator is itself a fraction.

• How do you simplify a complex fraction?

• Answer: To simplify a complex fraction, we can use the following steps:

  1. Simplify the numerator and denominator of each fraction independently.
  2. Multiply the numerator and denominator of the resulting fraction by the product of the denominators of the original fractions.
  3. Simplify the resulting fraction.

• What are some tips for simplifying complex fractions?

• Answer: Here are some tips for simplifying complex fractions:

  • Start by simplifying the numerator and denominator of each fraction independently. This will often make the fraction easier to work with.
  • When multiplying the numerator and denominator of the resulting fraction, be careful to distribute any negative signs.
  • If the resulting fraction is still complicated, you can try to factor the numerator or denominator.