Questions: Solve for (u). [ frac2u-5=frac63u-15-4 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

$Solve for (u). [ frac2u-5=frac63u-15-4 ] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".$

Transcript text: 4:01 PM Tue Jan 7 Done www-awu.aleks.com - Rational Expressions Solving a rationsl equation that simplifies to linear: Unilike binomial... Solve for $u$. \[ \frac{2}{u-5}=\frac{6}{3 u-15}-4 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $\square$ \[ u=[ \] No solution 므․ Explanation Check

Solution

Solution Steps

Step 1: Simplifying the Equation

We start with the equation: \[ \frac{2}{u-5} = \frac{6}{3u-15} - 4 \] Notice that $3u - 15$ can be factored as $3(u - 5)$. Thus, we can rewrite the equation as: \[ \frac{2}{u-5} = \frac{6}{3(u-5)} - 4 \]

Step 2: Eliminating Fractions

To eliminate the fractions, we can multiply both sides of the equation by $3(u - 5)$: \[ 3 \cdot 2 = 6 - 4 \cdot 3(u - 5) \] This simplifies to: \[ 6 = 6 - 12(u - 5) \]

Step 3: Solving for $u$

Rearranging the equation gives: \[ 6 = 6 - 12u + 60 \] This simplifies to: \[ 0 = -12u + 60 \] Solving for $u$ yields: \[ 12u = 60 \implies u = 5 \]

Final Answer

However, substituting $u = 5$ back into the original equation leads to a division by zero in the left-hand side, indicating that this value is not valid. Therefore, there are no solutions to the equation.

The final answer is: \[ \boxed{\text{No solution}} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!