#### Transcript of Rational&Radical Expressions

**Rational&Radical Expressions**

Rational Expression

Definition-Is an expression where one polynomial is divided by another.

Rule#1: The denominator

can not

equal zero.

Steps for Solving Rationals with same denominator

1:Add/subtract numerators

2:Write the sum/difference as the numerator over denominator

3:Reduce(if necessary)

Example

Problem: 5x-1/x+8 - 3x+4/x+8

(5x-1)-(3x+4)/x+8 what to do: subtract the like terms in numerator

5x-3x=2x -1-4=-5 Rewrite your answers as a fraction.

2x-5/x+8

Therefore 2x-5/x+8 is your answer.

Rational Expressions with different denominators

1:Factor each denominators

2:Find least common denominator

3:Rewrite expression with the least common denominator

4:Add/subtract numerators

5:Rewrite the sum/difference over common denominator

6:Reduce(if necessary)

Example

Problem: 5x-1/x^2-3x+2 +3/2x-4

Find LCD. For the first equation the Lcd is 2(x-1),(x-2)

5x-1/(x-1)(x-2)+3/2(x-1)(x-2)

Rewrite expression with LCD

2(5x-1)/2(x-1)(x-2)+3(x-1)/2(x-1)(x-2)

rewrite

2(5x-1)+3(X-1)/2(x1-1)(x-2)=

13x-5/2(x-1)(x-2)*which is the answer

Radical Expressions

A radical can be any root

For instance the square root of x+2=6 is a radical equation while the x+sqrt2=6 is not.

Goals&Issues

Goal is to get the variable by itself.

Common issue is to square terms not sides.

*SQUARE SIDES,NOT TERMS*

Rules

1:Isolate radical on one side of the expression

2:Square both sides of the expression to eliminate radical

3:Solve and simplify

4:Check answers by substituting them in the original equation

Examples

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