Questions: Solve for t. 8/(2t-8) - 4/(t-4) = 4

Solve for t. 8/(2t-8) - 4/(t-4) = 4
Transcript text: Solve for $t$. \[ \frac{8}{2 t-8}-\frac{4}{t-4}=4 \]
failed

Solution

failed
failed

Solution Steps

To solve the equation \(\frac{8}{2t-8} - \frac{4}{t-4} = 4\), we need to find a common denominator and then solve the resulting equation for \(t\).

  1. Identify the common denominator for the fractions.
  2. Combine the fractions over the common denominator.
  3. Simplify the equation and solve for \(t\).
  4. Check for any extraneous solutions by substituting back into the original equation.
Step 1: Identify the Common Denominator

To solve the equation \(\frac{8}{2t-8} - \frac{4}{t-4} = 4\), we first identify the common denominator for the fractions. The denominators are \(2t-8\) and \(t-4\). Notice that \(2t-8 = 2(t-4)\).

Step 2: Combine the Fractions

Rewrite the equation using the common denominator: \[ \frac{8}{2(t-4)} - \frac{4}{t-4} = 4 \] Multiply both sides by the common denominator \(2(t-4)\) to clear the fractions: \[ 8 - 4 \cdot 2 = 4 \cdot 2(t-4) \] Simplify: \[ 8 - 8 = 8(t-4) \] \[ 0 = 8(t-4) \]

Step 3: Solve for \(t\)

Solve the equation \(0 = 8(t-4)\): \[ 0 = 8(t-4) \] \[ t-4 = 0 \] \[ t = 4 \]

Step 4: Check for Extraneous Solutions

Substitute \(t = 4\) back into the original equation to check for extraneous solutions: \[ \frac{8}{2(4)-8} - \frac{4}{4-4} = 4 \] This results in division by zero, which is undefined. Therefore, \(t = 4\) is not a valid solution.

Final Answer

There is no solution to the equation \(\frac{8}{2t-8} - \frac{4}{t-4} = 4\).

\[ \boxed{\text{No solution}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Et 208V It A Rt Ω Pt W E1 V I1 A R1 150 Ω P1 w E2 V I2 A R2 8000 Ω P2 W E3 V I3 A R3 5050 Ω P3 W E4 V I4 A R4 65500 Ω P4 W E5 V I5 A R5 2500 Ω P5 W E6 V I6 A R6 2300 Ω P6 W
failedAnswered
a. Change the chart type to a Clustered Bar chart. b. Use Actual Project Hours as the chart title. c. Add a primary horizontal axis title to the chart, using Hours as the axis title text. d. Add data labels in the center of each bar.
failedAnswered
Suponga una economía de la que sabemos que existe tipo de cambio fijo de 1500diner/. Explique y grafique (IS/LM y mercado monetario) que efecto tendría en la tasa de interés si el tipo de cambio actual se encuentra en 800diner/.
failedAnswered
Determine which form of a line the given equation is in. Then, determine the slope, the x-intercept, and the y-intercept. Select the answer choice that correctly identifies each of these. 5x-2y=5 It is in slope-intercept form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0,5). It is in standard form; the slope is m=-2, the x-intercept is (1,0), and the y-intercept is (0, 5/2). It is in standard form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2). It is in point-slope form; the slope is m=5/2, the x-intercept is (1,0), and the y-intercept is (0,-5/2).
failedAnswered
A line has a slope of -1/2 and passes through the point (-12,0). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.