SECTION 6 4 SOLVING RATIONAL EXPRESSIONS REVIEW NON

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SECTION 6. 4 SOLVING RATIONAL EXPRESSIONS

SECTION 6. 4 SOLVING RATIONAL EXPRESSIONS

REVIEW) NON PERMISSIBLE VALUES (NPV) Any value of “x” (Variable) that makes the denominator

REVIEW) NON PERMISSIBLE VALUES (NPV) Any value of “x” (Variable) that makes the denominator equal to zero Ie: Find the NPV Look at the Denominator Make each denominator equal to zero and solve for “x”

I) SOLVING RATIONAL EQUATIONS “Solving” means finding the value of “x” where both sides

I) SOLVING RATIONAL EQUATIONS “Solving” means finding the value of “x” where both sides of an equation are equal On a graph, it’s where the two functions cross/intersect each other Steps to Solve Algebraically � Find the NPV (Non-Permissible Values) � Find the LCD � Multiply all terms by LCD to cancel out the Denominator � Simplify and Solve for ‘x’ � ‘x’ can not be the same as the NPV (Extraneous Root)

NOTE: SOLVING VS SIMPLIFYING Simplifying: form Reducing an equation to a simplified Solving: Finding

NOTE: SOLVING VS SIMPLIFYING Simplifying: form Reducing an equation to a simplified Solving: Finding a value for the variable so that both sides of the equation will be EQUAL!!! �Find the L. C. D. �Multiply “ALL” terms by LCD to cancel out the denominator �Check your answer by plugging it back into the equation �Find the N. P. V.

EX: SOLVE FOR “X” LCD: Multiply all terms by LCD, not just terms with

EX: SOLVE FOR “X” LCD: Multiply all terms by LCD, not just terms with a denominator! NPV

PRACTICE: SOLVE EACH OF THE FOLLOWING LCD:

PRACTICE: SOLVE EACH OF THE FOLLOWING LCD:

CHALLENGE: SOLVE LCD:

CHALLENGE: SOLVE LCD:

II) EQUATIONS WITH EXTRANEOUS SOLUTIONS OR NO SOLUTIONS Extraneous solutions are answers that are

II) EQUATIONS WITH EXTRANEOUS SOLUTIONS OR NO SOLUTIONS Extraneous solutions are answers that are not allowed This happens when the solution is the same as the NPV An equation will have no solutions when both sides are not equal when all the variables are eliminated In contrast, an equation will have infinite solutions when both sides are equal when all variables are gone When terms in a binomial are reversed, you get a negative in front

EX: SOLVE AND FIND THE NPV Extraneous Root!! No Solutions because both sides are

EX: SOLVE AND FIND THE NPV Extraneous Root!! No Solutions because both sides are not equal!!

PRACTICE: SOLVE & FIND THE NPV The terms in the binomial are switched Both

PRACTICE: SOLVE & FIND THE NPV The terms in the binomial are switched Both sides are exactly equal There are no variables left No matter what the value of “x” and both sides are NOT equal is, both sides are always the same Answer will be no real solutions Solution will be all real numbers

PRACTICE: SOLVE Find the NPV: Find the LCD: The solution is the same as

PRACTICE: SOLVE Find the NPV: Find the LCD: The solution is the same as the extraneous root, so, no solutions

III) SOLVING RATIONAL EQUATIONS BY GRAPHS The left side of the equation is y

III) SOLVING RATIONAL EQUATIONS BY GRAPHS The left side of the equation is y 1. The right side of the equation is y 2 Rational Function NPV: Straight Line y 12 Solving means finding the point where both functions intersect each other 8 4 x -30 -25 -20 -15 -10 -5 0 -4 -8 -12 5 10 15

EX: SOLVE Find the NPV: Find the LCD: Multiply all terms by the LCD

EX: SOLVE Find the NPV: Find the LCD: Multiply all terms by the LCD Solve for “x” The solution is not the same as the NPV

HOMEWORK: Assignment 6. 4

HOMEWORK: Assignment 6. 4