Rational Expression

Complex Fractions

  • Simplify

LDC Method

MRB Method

1) Find the LCD

2) Mul fraction by LDC/LCD

3) simplify

1) Add/Sub numerator & Denominator to one tern (using the LCD)

2) MBR (mul across)

3) simplify

Rational Expressions

Quotient of 2 polynomials

  • Adding & Subtracting

    • Find the LCD

    • Create the fraction with common denominator

    • Add/Sub numerators

    • Simplify

  • Multiplying/Dividing

    • Multiply across and simplyfy

      • BUT

      • If there is +- then you have to distribute

    • Divide MBR

      • BUT
        if there is +- cross out repeats that cancel out

Solving Rational Expressions

Rational Equation : Equation that contains 1+ rational expressions

values are eliminated bc of the restrictions on the Domain : extraneous

so’s

  1. Find Restrictions (set denominator = 0 & solve)

  2. Solve

    1. Proportion

    2. cross multiply and solve

      Ex) 2/3x + 1/6 = 4/3x

      1. LCD= 6x SO put 6x/1 and mul by all

      2. (2/3x + 1/6 = 4/3x) 6x/1

      3. 2/3x * 6x/1 + 1/6 * 6x/1 = 4/3x* 6x/1

  3. Mul by the LCD

    1. (+-) to eliminate the fraction s

      Ex) x-3/x+5 = x/x+2

      1. Extraneous : -5,-2

      2. (x-3)(x+2) = x(x-5)

Variation

  • Direct Variation

    • Relationship (x,y) is constant

    • y=kx

      • K= constant variable

      • Solve for k=y/x

  • Indirect

    • 2 quantities vary inversely (one inc one dec) poportionally

      • y=k/x

        • Solve for k=yx

  • Combined Variations

    2+ variables

z varies jointly with x and y

z=kxy

z varies jointly with x and y and inversely with w

z=kxy/w

z varies directly with x and inversely with wy

z=kx/wy

Graphing

Parent Function

f(x)=1/x

Graph

f(x)=1/x

Domain

(-∞,0) u (0,∞)

Range

(-∞,0) u (0,∞)

Asymptote’s

VA: x=0 HA: y=0

x-intercept

N/A

y-intercept

N/A

Interval increasing

N/A

Interval Decreasing

(-∞,0) u (0,∞)

Inverse (switch x & y)

x=1/t → xy=1 → y=1/x