Simplifying Rational Expressions
Simplifying rational expressions is like reducing rational numbers. First fully factor the numerator and denominator and then cancel all the common
Subject: cancel
Transcript: 2 TIMES 3 TIMES 7. 70 IS 2 TIMES 5 TIMES 7. NOW WE CAN CANCEL. REMEMBER, WHEN WE CANCEL, WE'RE TAKING OUT FACTORS OF 1. SO WE CAN CANCEL 2/2. WE CAN
Rational Expressions that Equal - 1
Rational expressions that equal -1 are recognizable: the terms in the numerator are identical to the terms in the denominator except for their signs, which are opposite.
Subject: cancel
Transcript: 'T BE FACTORED, AND THERE ARE NO FACTORS WE CAN CANCEL. BUT SUPPOSE WE FACTOR NEGATIVE 1 FROM THE DENOMINATOR. WE GET NEGATIVE 1 TIMES NEGATIVE B PLUS A
Subtracting Rational Expressions
Rational expressions with the same number in the denominator are subtracted.
Subject: cancel
Transcript: NUMERATOR. 5N MINUS 5 CAN BE FACTORED. THE FACTORS OF THE NUMERATOR ARE 5 AND N MINUS 1. THE DENOMINATOR IS STILL N MINUS 1. LOOK AT THAT, WE CAN CANCEL THE N
Solving Equations That Include Rational Expressions
To solve an equation with a rational expression, rewrite the equation to get rid of the fractions then solve the new equation. The same process is used to solve linear equations that contain rational expressions. If the solution makes any denominato...
Subject: cancel
Transcript: /2. CANCEL. MULTIPLY. THE RESULT IS 3X. NOW, 6 TIMES X/3. CANCEL. MULTIPLY. IT'S 2X. NEXT, MULTIPLY THE RIGHT SIDE OF THE EQUATION. THE 6'S CANCEL OUT
Practical Problem: How Much Land to Buy
A practical problem involving the purchase of land is presented. The available information is organized into a table, an equation is written, then solved using the least common denominator to get a quadratic equation, and the solution checked.
Subject: cancel
Transcript: , THE X MINUS 100'S CANCEL. THE RESULT IS 400X. NEXT WE'LL WORK ON THE RIGHT SIDE. WHEN WE MULTIPLY THE LEAST COMMON DENOMINATOR BY THE FIRST TERM, THE X
Factoring Before Simplifying a Rational Expression
Examples of factoring before simplifying a rational expression are presented.
Subject: cancel
Transcript: HERE'S ANOTHER EXAMPLE. THERE'S A BINOMIAL IN THE NUMERATOR AND A TRINOMIAL IN THE DENOMINATOR. BE CAREFUL HERE. REMEMBER, WE CAN'T CANCEL TERMS
Practical Problem: Two Solutions for a Work Problem
A practical work problem that requires finding out how long it will take two workers with different work speeds to complete a task is solved using an equation with a rational expression. Two different approaches to finding the solution to this probl...
Subject: cancel
Transcript: THE LEFT SIDE. 120 TIMES X/40. CANCEL. THEN MULTIPLY. THE RESULT IS 3X. NEXT, WE'LL MULTIPLY 120 BY X/24. AFTER WE CANCEL AND MULTIPLY, WE GET 5X
Practical Problem: Two solutions for a Pool Problem
A work problem is presented to determine how long it will take to fill a pool that has an open drain.
Subject: cancel
Transcript: THE LEFT SIDE, WE'LL MULTIPLY THE FIRST TERM. CANCELING COMMON FACTORS GIVES US 9X. NEXT, WE'LL MULTIPLY THE SECOND TERM. CANCELING COMMON FACTORS GIVES
Factoring before Multiplying Rational Expressions
If a rational expression is more complicated, factoring before multiplying might be indicated.
Subject: cancel
Transcript: CHORE. AFTER THAT, WE'D STILL HAVE TO MULTIPLY THE DENOMINATORS, THEN FACTOR, AND FINALLY REDUCE. SO WE'LL TRY CANCELING FIRST, THEN MULTIPLYING. BUT
Multiplying Rational Expressions
Demonstration of the procedure for multiplying rational expressions.
Subject: cancel
Transcript: NUMBERS. INSTEAD OF MULTIPLYING FIRST, WE CAN CANCEL FIRST. 2 AND 4 HAVE A COMMON FACTOR OF 2. CANCELING THE 2'S GIVES US A 1 IN THE SECOND NUMERATOR AND A