Question

the movement of the progress bar may be uneven because questionssolve the equation:$\frac{6}{x+5} = \frac{3}{x-10}$what are the solutions?○ $x = 25$ only○ $x = 5$○ $x = -20$○ $x = -5, 10$

Explanation:

Step1: Cross-multiply to eliminate fractions

$6(x-10) = 3(x+5)$

Step2: Distribute coefficients

$6x - 60 = 3x + 15$

Step3: Isolate x terms

$6x - 3x = 15 + 60$

Step4: Simplify both sides

$3x = 75$

Step5: Solve for x

$x = \frac{75}{3} = 25$

Step6: Check for extraneous solutions

Substitute $x=25$ into original equation: $\frac{6}{25+5}=\frac{6}{30}=0.2$, $\frac{3}{25-10}=\frac{3}{15}=0.2$. Valid; $x=10,-5$ make denominators 0, so invalid.

Answer:

x = 25 only