/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 72 Simplify each complex rational e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 72

Simplify each complex rational expression. $$\frac{\frac{x+h}{x+h+1}-\frac{x}{x+1}}{h}$$

Short Answer

Expert verified
The simplified expression is \( \frac{1}{(x+h+1)(x+1)}\).

Step by step solution

01

Find Common Denominator

The first step is to find a common denominator for the fractional expressions in the numerator. This is done by multiplying the denominators of the two fractions together, which results in \((x+h+1)(x+1)\). Now, rewrite the fractional expressions in the numerator with the common denominator: \(\frac{(x+h)(x+1)-(x)(x+h+1)}{(x+h+1)(x+1)}\). Hence, the whole fraction becomes \(\frac{\frac{(x+h)(x+1)-(x)(x+h+1)}{(x+h+1)(x+1)}}{h}\).
02

Simplifying the numerator

Next step is to distribute and combine like terms in the numerator. So the numerator becomes \(\frac{x^2+xh+x+h-x^2-xh-x}{(x+h+1)(x+1)}\) which simplifies to \( \frac{h}{(x+h+1)(x+1)}\). Therefore, the whole fraction simplifies to \( \frac{\frac{h}{(x+h+1)(x+1)}}{h}\).
03

Cancel out the \(h\)

The final step is to cancel out \(h\) from the numerator and denominator so that \(h/h = 1\). So the final result of simplification is \( \frac{1}{(x+h+1)(x+1)}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify using properties of exponents. $$\frac{20 x^{\frac{1}{2}}}{5 x^{4}}$$

Simplify using properties of exponents. $$\left(3 x^{\frac{2}{3}}\right)\left(4 x^{\frac{3}{4}}\right)$$

Why must \(a\) and \(b\) represent non negative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b ?}\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I simplified the terms of \(2 \sqrt{20}+4 \sqrt{75},\) and then I was able to add the like radicals.

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4} y^{\frac{1}{3}}}}{x^{-\frac{3}{4}}}\right)^{-6} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.