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Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Finish the assignment

Exercise 19 Page 966

Factor the denominators, and multiply both sides of the equation by the least common denominator.

Practice makes perfect

We want to solve the given rational equation. 3/2x+10+5/4=7/x+5 We will start by factoring the denominators to find a least common denominator (LCD). Note that the second and the third denominator are already factored. Let's factor the first one.

2x+10

FactorOut

Factor out 2

2(x+5)

We can now rewrite the given expression. 3/2x+10+5/4=7/x+5 ⇕ 3/2 (x+5)+5/4=7/(x+5) The LCD is 4 (x+5) because it is the least common multiple of the denominators. We will solve the equation by multiplying each side by the LCD to clear denominators.

3/2(x+5)+5/4=7/x+5

MultEqn

LHS * 4 (x+5)=RHS* 4 (x+5)

(3/2(x+5)+5/4)* 4 (x+5)=7/x+5* 4 (x+5)

▼

Multiply

Distr

Distribute 4(x+5)

3/2(x+5)* 4(x+5)+5/4 * 4(x+5)=7/x+5 * 4(x+5)

CancelCommonFac

Cancel out common factors

3/2(x+5)* 4(x+5)+5/4 * 4(x+5)=7/x+5 * 4(x+5)