Explain how find the LCD of a rational equation Tell why it is necessary to chec

Question

Explain how find the LCD of a rational equation Tell why it is necessary to check your solutions when solving a rational equation. Give an example in your explanation. A'h-mose (more commonly referred to as Ahmes) was an Egyptian scribe who copied an earlier mathematics text on papyrus in 1650 B.C. Papyrus was a writing material made from the papyrus plant that was used by the ancient Egyptians. A'h-mose's papyrus was purchased by the English Egyptologist A. Henry Rhind. As a result, it has come to be called the Rhind Papyrus. A'h-mose began his text with a table of fractions and an explanation of the Egyptian method of using fractions. The ancient Egyptians defined all fractions, with the single exception of the fraction 2/3 in terms of unit fractions. That is, they only used fractions with a numerator of one. For example, instead of writing 3/4 they wrote l/2+l/4 Instead of writing 5/6, they wrote 1/2+ 1/3.

Explanation / Answer

1) LCD of arational equation : example

2/(x^2 +x +9) + 2/(3x+9)

Now x^2 + x+9 =(x+3)(x+3)

3x+9 = 3(x+3)

So,The factors that appear in each denominator are 3 and (x+3) and the LCD is 3(x+3)^2

So, 2/(x^2 +x +9) + 2/(3x+9) = [ 2(3) + 2(x+3)]/3(x+3)^2

= (6 +2x +6)/3(x+3)^2

= (2x+12)/3(x+3)^2

.

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