(Q15.) Add Rational Expressions

TL;DR

Learn how to add fractions with different denominators by finding a common denominator and simplifying the result.

Transcript

here we're going to add these twelve a fractions but unfortunately as we can see they do not have the same denominators yet remember whenever one to add wasn't read fractions the denominators has to be the same right so to figure out the same denominator this is what we do we look at the denominator of this which is 2x squared minus 9x minus 5 we n... Read More

Key Insights

• 🪜 Fractions with different denominators cannot be added directly; a common denominator is required.
• 🧑‍🏭 To find a common denominator, factor the denominators and multiply accordingly.
• 🧑‍🏭 The resulting fraction can be simplified by factoring out any common factors in the numerator and denominator.

Questions & Answers

Q: How do you add fractions with different denominators?

To add fractions with different denominators, find a common denominator by factoring the denominators and multiplying the numerators and denominators accordingly.

Q: Why is it necessary to find a common denominator before adding fractions?

It is necessary to find a common denominator because fractions with different denominators represent different sized parts, and adding them directly would lead to incorrect results.

Q: How do you factor a polynomial expression?

Factoring a polynomial expression involves finding the factors that, when multiplied, yield the original expression. In this case, the tato method is used to factor a trinomial by finding two numbers that when multiplied give the constant term and when added give the coefficient of the middle term.

Q: What do you do after finding the common denominator and adding the numerators?

After finding the common denominator and adding the numerators, simplify the resulting fraction by factoring out any common factors in the numerator and denominator.

Summary & Key Takeaways

• Fractions with different denominators cannot be added directly.

• To add fractions with different denominators, find a common denominator by factoring the denominators.

• Multiply the numerator and denominator of each fraction by the necessary factors to make the denominators the same.

• Combine the numerators and simplify the resulting fraction by factoring out any common factors.