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## What is the Lowest Common Denominator (LCD)?

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**5.3 – Addition & Subtraction of Rational Expressions**What is the Lowest Common Denominator (LCD)?**5.3 – Addition & Subtraction of Rational Expressions**What is the Lowest Common Denominator (LCD)?**5.3 – Addition & Subtraction of Rational Expressions**What is the Lowest Common Denominator (LCD)?**5.3 – Addition & Subtraction of Rational Expressions**Examples (Like Denominators):**5.3 – Addition & Subtraction of Rational Expressions**Examples (Like Denominators):**5.3 – Addition & Subtraction of Rational Expressions**Examples (Like Denominators):**5.3 – Addition & Subtraction of Rational Expressions**Examples: 15**5.3 – Addition & Subtraction of Rational Expressions**Examples: 40x2**5.3 – Addition & Subtraction of Rational Expressions**Examples:**5.3 – Addition & Subtraction of Rational Expressions**Examples:**5.3 – Addition & Subtraction of Rational Expressions**Examples:**5.3 – Addition & Subtraction of Rational Expressions**Examples: continued**5.3 – Addition & Subtraction of Rational Expressions**Examples:**5.3 – Addition & Subtraction of Rational Expressions**Examples: continued**5.4 – Complex Fractions**Complex Fractions Defn: A rational expression whose numerator, denominator, or both contain one or more rational expressions.**5.4 – Complex Fractions**LCD: 12, 8 24 LCD: 24 24 2 3**5.4 – Complex Fractions**LCD: y y–y**5.4 – Complex Fractions**LCD: 6xy 6xy 6xy**5.4 – Complex Fractions**Outersover Inners LCD: 63**5.4 – Complex Fractions**Outersover Inners**5.5 – Equations with Rational Expressions**Solve for a LCD: abx**5.6 – Applications**Problems about Numbers If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x**Time to sort one batch (hours)**Fraction of the job completed in one hour 5.6 – Applications Ryan Mike Together Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch? 2 3 x**Time to sort one batch (hours)**Fraction of the job completed in one hour 5.6 – Applications Ryan Mike Together Problems about Work 2 3 x 6x LCD = hrs.**Time to mow one acre (hours)**Fraction of the job completed in one hour 5.6 – Applications James Andy Together James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together? 2 8 x**Time to mow one acre (hours)**5.6 – Applications Fraction of the job completed in one hour James Andy Together 2 8 x LCD: 8x hrs.**Time to pump one basement (hours)**Fraction of the job completed in one hour 5.6 – Applications 1st pump 2nd pump Together A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone? 12 x**Time to pump one basement (hours)**Fraction of the job completed in one hour 5.6 – Applications 1st pump 2nd pump Together 12 x**5.6 – Applications**LCD: 60x hrs.**5.6 – Applications**Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?**5.6 – Applications**A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles. x t 450 mi t x + 15 600 mi**5.6 – Applications**450 mi x t t x + 15 600 mi LCD: x(x + 15) x(x + 15) x(x + 15)**5.6 – Applications**x(x + 15) x(x + 15) Motorcycle Car**5.6 – Applications**A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed = x t 22 mi x - 5 t 42 mi x + 5**5.6 – Applications**boat speed = x x - 5 t 22 mi 42 mi x + 5 t LCD: (x – 5)(x + 5) (x – 5)(x + 5) (x – 5)(x + 5)**5.6 – Applications**(x – 5)(x + 5) (x – 5)(x + 5) Boat Speed**5.7 – Division of Polynomials**Dividing by a Monomial**5.7 – Division of Polynomials**Dividing by a Monomial**5.7 – Division of Polynomials**Review of Long Division**5.7 – Division of Polynomials**Long Division**5.7 – Division of Polynomials**Long Division