Rational Equations Answers
Solve and check The solution is c =
PENDING
Name the extraneous solution(s) to the equation.✔ x = 0x = 1x = 8x = 0, x = 1, and x = 8x = 1 and x = 8There are no extraneous
After multiplying each side of the equation by the LCD and simplifying, the resulting equation is .
Solve and check: 1 x + 3 = x + 10 x − 2 From least to greatest, the solutions are x = and x = ⇒ -4.
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The student is not correct in claiming that 𝑎 = − 2 a=−2 is a solution. The original equation is 3 𝑎 + 2 − 6 𝑎 𝑎 2 − 4 = 1 𝑎 − 2 a 2 −4 3a+2−6a = a−2 1 . Simplifying the numerator on the left gives − 3 𝑎 + 2 −3a+2, and factoring the denominator gives ( 𝑎 − 2 ) ( 𝑎 + 2 ) (a−2)(a+2). Multiplying both sides by 𝑎 − 2 a−2 (assuming 𝑎 ≠ 2 a =2) leads to the equation − 3 𝑎 + 2 𝑎 + 2 = 1 a+2 −3a+2 =1, which simplifies to 𝑎 = 0 a=0. The value 𝑎 = − 2 a=−2 is not valid because it makes the denominators 𝑎 2 − 4 a 2 −4 and 𝑎 + 2 a+2 equal to zero, resulting in division by zero. Therefore, 𝑎 = − 2 a=−2 is an extraneous solution, and the correct solution to the original equation is 𝑎 = 0 a=0.
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What are the solutions to the equation?
⇒ -4
Name the true solution(s) to the equation.x = 0x = 1x = 8x = 0, x = 1, and x = 8✔ x = 1 and x = 8There are no solutions.
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