Questions: Solve the rational equation. 5/(x-6)^2=0 -6 6 5 ∅

Solve the rational equation. 5/(x-6)^2=0 -6 6 5 ∅
Transcript text: Question 2 8.33 / 8.33 pts Solve the rational equation. \[ \frac{5}{(x-6)^{2}}=0 \] $\{-6\}$ $\{6\}$ $\{5\}$ $\varnothing$
failed

Solution

failed
failed

Solution Steps

To solve the rational equation \(\frac{5}{(x-6)^{2}}=0\), we need to determine when the numerator is zero. However, since the numerator is a constant (5), it will never be zero. Therefore, the equation has no solution.

Step 1: Analyze the Equation

We start with the rational equation

\[ \frac{5}{(x-6)^{2}}=0. \]

To solve this equation, we need to determine when the left-hand side equals zero.

Step 2: Examine the Numerator

The numerator of the fraction is 5, which is a constant. Since a fraction is equal to zero only when its numerator is zero, we check:

\[ 5 = 0. \]

This statement is false, indicating that the numerator can never be zero.

Step 3: Conclusion

Since the numerator is never zero, the equation

\[ \frac{5}{(x-6)^{2}}=0 \]

has no solutions. Therefore, the solution set is empty.

Final Answer

\(\boxed{\varnothing}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the equation by the square root property [ (x-7)^2=64 ] What is the solution set?
failedAnswered
Find the critical value for a left-tailed test using the F distribution with α=0.025, degrees of freedom in the numerator =20, and degrees of freedom in the denominator =50. A portion of the table of critical values of the F-distribution is provided. What is the critical value? (Round to two decimal places as needed.)
failedAnswered
Perform the operation if possible. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3[3 -1 -3; -4 3 -1; -3 -5 3] + 4[2 1 4; 4 2 6; 1 1 2] = □ (Type an integer or simplified fraction for each matrix element.) B. The operations are not defined.
failedAnswered
Para chamar a atenção de seus clientes, uma empresa mandou instalar no pátio um monumento com o seu logotipo formado por paralelepípedos retângulos e com as medidas indicadas no desenho abaixo. V=6.3 .8 V=144 8 m V=3+2: 3 V=18
failedAnswered
The students in a science class took a field trip to a pond. They were all asked to catch a frog and measure its weight (in ounces). The following histogram displays the results. How many frogs weigh greater than 14.5 ounces?