Standard Form of a Linear Equation
The standard form for a linear equation is detailed.
Subject: fraction
Transcript: EQUATION. X AND Y ARE VARIABLES. A, B, AND C CAN BE ANY REAL NUMBERS. THEY CAN BE POSITIVE, NEGATIVE, FRACTIONS, OR 0. BUT A AND B CANNOT BOTH BE 0 AT THE
Simplifying Rational Expressions
Simplifying rational expressions is like reducing rational numbers. First fully factor the numerator and denominator and then cancel all the common factors. The process is illustrated step by step.
Subject: fraction
Transcript: LET'S TAKE A LOOK AT SIMPLIFYING RATIONAL EXPRESSIONS. IT'S JUST LIKE SIMPLIFYING OR REDUCING RATIONAL NUMBERS. WE CAN WORK WITH A FRACTION LIKE
Solving an Equation with the Least Common Denominator: Another Practice Problem
A problem is presented to practice solving an equation using the least common denominator to get a quadratic equation.
Subject: fraction
Transcript: THE LEAST COMMON DENOMINATOR OF THE FRACTIONS IN THE EQUATION IS 5X TIMES X PLUS 2. SO WE'LL MULTIPLY BOTH SIDES OF THE EQUATION BY THESE FACTORS
Two Approaches for Dividing Radicals
squares. Another guideline for simplifying radicals is introduced: all fractions must be reduced to lowest terms.
Subject: fraction
Transcript: AS WE'RE DIVIDING A RADICAL BY ANOTHER RADICAL, WE CAN DIVIDE THE NUMERATOR BY THE DENOMINATOR AS WE WOULD IN ANY FRACTION. THE SQUARE ROOT OF 36
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
Subject: fraction
Transcript: SOLVING EQUATIONS WITH RATIONAL EXPRESSIONS IS SIMILAR TO SOLVING EQUATIONS THAT HAVE FRACTIONS. TO SOLVE AN EQUATION LIKE THIS, WE FIND THE LEAST
Solving Systems with Fractions in the Equations
Systems of equations that contain fractions can be difficult to work with. Clearing the fractions in such a system by multiplying each equation by
Subject: fraction
Transcript: NARRATOR: WE'VE SOLVED SYSTEMS WITH FRACTIONS IN THE SOLUTION. NOW LET'S LOOK AT SYSTEMS WITH FRACTIONS IN THE EQUATIONS. HOW DO WE SOLVE A SYSTEM
Solving Inequalities
The procedure for solving an inequality by performing the same operation on each side of the statement.
Subject: fraction
Transcript: PROBLEM. THE VARIABLE IS PART OF A FRACTION. WE CAN GET RID OF THE FRACTION AND ISOLATE THE VARIABLE BY MULTIPLYING BY 2. THE SOLUTION IS X IS LESS THAN OR
Radicand Divided by Another Radicand, A
Simplifying a radical expression by dividing the radical in the numerator by the radical in the denominator.
Subject: fraction
Transcript: SIMPLIFIED. NOW THE SQUARE ROOT OF 3 APPEARS IN THE NUMERATOR AND THE DENOMINATOR. WE CAN CANCEL THESE FACTORS JUST AS WE WOULD IN ANY FRACTION. THE ANSWER IS
Negative Exponents in the Denominator
Simplifying an expression with a negative exponent in the denominator, and a formula that makes it easier.
Subject: fraction
Transcript: DENOMINATOR, WE GET 1 OVER 1 OVER X TO THE 12TH. THAT'S THE SAME AS 1 DIVIDED BY X TO THE 12TH. WE DIVIDE FRACTIONS BY FINDING THE RECIPROCAL OF THE DIVISOR AND
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: fraction
Transcript: DENOMINATOR OF THE FRACTIONS. IT'S X TIMES X MINUS 100. SO WE'LL MULTIPLY BOTH SIDES OF THE EQUATION BY THESE TWO FACTORS. WE'LL BEGIN ON THE LEFT SIDE. HERE