Determine the Domain of the Fraction Equation: 5x/(2(x-7)) = 10/(8x)

Question

Find the domain

(no need to resolve)

5x2(x7)=108x \frac{5x}{2(x-7)}=\frac{10}{8x}

Video Solution

Solution Steps

00:10 We're figuring out the range without solving the whole equation.
00:15 To find the range, let's make sure the denominator isn't zero.
00:19 Remember, dividing by zero isn't allowed.
00:23 First, we'll set the denominator equal to zero and check it out.
00:28 Let's simplify things as much as possible.
00:32 Next step, we isolate X.
00:37 Great! We've found the range from the first fraction.
00:41 Time to check the second denominator. Set that to zero too.
00:46 Again, let's focus on isolating X.
00:50 And there we have it. This is the second substitution range.
00:54 And that's how we solve the question. Well done!

Step-by-Step Solution

To find the domain of the rational equation 5x2(x7)=108x \frac{5x}{2(x-7)} = \frac{10}{8x} , we need to ensure neither denominator equals zero.

Start by examining the first denominator, 2(x7) 2(x-7) :

  • Set 2(x7)=0 2(x-7) = 0 .
  • Solve for x x to find x7=0 x - 7 = 0 , resulting in x=7 x = 7 .

Next, examine the second denominator, 8x 8x :

  • Set 8x=0 8x = 0 .
  • Solve for x x to find x=0 x = 0 .

Therefore, the function is undefined at x=0 x = 0 and x=7 x = 7 . These values should be excluded from the domain.

Thus, the domain of the given rational equation is all real numbers except where x=0 x = 0 and x=7 x = 7 .

This corresponds to the correct answer choice: x0,x7 x \neq 0, x \neq 7 .

Answer

x0,x7 x≠0,x≠7