Studdy AI Logo
Math

QuestionMultiply the numerator and denominator of xx−2−1x+12xx−2\frac{\frac{x}{x-2}-\frac{1}{x+1}}{\frac{2 x}{x-2}} by which expression to simplify?

Studdy Solution

STEP 1

Assumptions1. We are allowed to multiply the same expression into both the numerator and the denominator of the given expression. . The goal is to simplify the given expression.

STEP 2

The given expression is a complex fraction, which is a fraction where the numerator, the denominator, or both contain fractions. To simplify complex fractions, we can multiply the numerator and the denominator by the least common denominator (LCD) of all the fractions within the complex fraction.

STEP 3

First, we need to identify the denominators of the fractions within the complex fraction.The denominators are (x−2)(x-2), (x+1)(x+1), and (x−2)(x-2).

STEP 4

The least common denominator (LCD) is the least common multiple (LCM) of the denominators. In this case, since the denominators (x−2)(x-2) and (x+1)(x+1) do not have any common factors other than1, the LCD is simply the product of the denominators, which is (x−2)(x+1)(x-2)(x+1).

STEP 5

Now, we multiply the numerator and the denominator of the complex fraction by the LCD, (x−2)(x+1)(x-2)(x+1).
xx−2−1x+12xx−2×(x−2)(x+1)(x−2)(x+1)\frac{\frac{x}{x-2}-\frac{1}{x+1}}{\frac{2 x}{x-2}} \times \frac{(x-2)(x+1)}{(x-2)(x+1)} This is the expression we would multiply into the numerator and denominator of the expression to simplify it.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord