Recall from section 1.2 that an equation that contains one or more rational expr

Question

Recall from section 1.2 that an equation that contains one or more rational expressions is called a rational equation. It is easiest to solve rational equation if the fractions are eliminated. This can be done by multiplying each side of the equation by the least common denominator (LCD) Remember that when you multiply each side by the LCD, each term on eackh side must be multiplied by the LCD. Consider the following 1. Open Ended Write a rational equation that can be solved by first multiplying each side by 5(a+2) 2. Explain why the equation x + 1+-has no solution. 3. State what expression by which you multiply each side of -33 in order to solve the equation. What value(s) of xcannot be a solution?

Explanation / Answer

1) rational function that can be solved by multiplying each side by 5 (a+2)

2/5 + 3 / (a+2) = 1

multiplying both sides by 5 (a+2)

2 (a+2) + 3 (5) = 5 (a+2)

2a + 4 + 15 = 5a + 10

- 3a = -9

a = 3

2) x + 1/ (x-1) = 1 + 1 / (x-1)

multiplying entire equation by (x-1)

x (x-1) + 1 = 1 (x-1) + 1

subtracting 1 from both sides

x(x-1) = 1 (x-1)

x^2 -x = x -1

x^2 - 2x + 1 = 0

x = 1

if we will plug x =1 in the original equation the denominator will become 0

hence, this equation has no solution

3) x/ (x-3) +1/3 =1

we multiply both sides by

3 (x-3)

in order to solve the equation

x = 3 cannot be a solution

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.