Simplify each expression, using only positive exponents in the answer. (x^-2+y^-2)/(x^-1+y^-1)

Name: Problem 59, Chapter 6: Beginning and Intermediate Algebra
Uploaded: 2022-02-17T06:49:23-08:00
Duration: 1 min 10 s
Channel: Yujie Wang
Description: Simplify each expression, using only positive exponents in the answer. (x^-2+y^-2)/(x^-1+y^-1)

step 1 Okay, so simplify this expression, use only positive exponents in the answer. So x to the minus

Simplify each expression, using only positive exponents in...

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Key Concepts

Laws of Negative Exponents

This concept explains that a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, any term of the form a^(-n) can be rewritten as 1/(a^n). This is essential in rewriting expressions to have only positive exponents, which is often a desired format in algebra.

Common Denominator and Combining Fractions

When working with fractions that have different denominators, finding a common denominator allows the expressions to be combined into a single fraction. This is particularly useful when both the numerator and the denominator of a larger fraction contain sums of fractions. By rewriting these fractions with a common denominator, one can simplify the expression more easily.

Simplifying Complex Rational Expressions

This concept involves reducing an expression that has fractions within fractions. The process typically includes rewriting inner negative exponents as reciprocals, combining like terms, and then simplifying by multiplying the numerator and denominator by a common factor. This method enables a clearer view of the overall structure of the expression and assists in reducing it to a simpler form with positive exponents.

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