SOLUTION: 1-2/4t-1=8/(4t-1)^2 It says to type the answer as an integer or simplified fraction

Algebra.Com
Question 349209: 1-2/4t-1=8/(4t-1)^2
It says to type the answer as an integer or simplified fraction
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
If the equation is:

then please put multiple term numerators and denominators in parentheses.

There are several ways to solve this equation. The shorter ways are based on noticing that either or just 4t-1 are expressions common in the equation. So we can used "clever", temporary substitutions to make the solution easier. Here are 3 solutions, 2 shorter ones and one long, "unclever", straightforward solution:
  1. Use a substitution for . Let . Then your equation becomes:

    The equation is now a fairly simple equation to solve (for q):


    4q - 1 = 0 or 2q + 1 = 0
    q = 1/4 or q = -1/2
    We have solutions for q but we want solutions for t. So we just substitute back in for q:
    or
    4t- 1 = 4 or 4t-1 = -2
    4t = 5 or 4t = -1
    t = 5/4 or t = -1/4
  2. Use a substitution for 4t-1. Let q = 4t-1. Substituting this into your equation becomes:

    To solve this, we'll start by multiplying both sides by :

    Subtract 8 from each side:


    q - 4 = 0 or q - 2 = 0
    q = 4 or q = -2
    Now we substitute back in for q:
    4t-1 = 4 or 4t-1 = -2
    4t = 5 or 4t = -1
    t = 5/4 or t = -1/4
  3. The long way with no substitutions. We'll start by multiplying both sides by giving:

    Simplifying we get:


    Subtract 8 from each side:


    4t - 5 = 0 or 4t + 1 = 0
    4t = 5 or 4t = -1
    t = 5/4 or t = -1/4

Note that all three solutions gave the same results. Keep your eyes open for repeated expressions like there were in this problem. The solutions whichtook advantage of the repeated expressions in your equation made the solution easier. (With a little practice you will eventually be able to do these without actually using a temporary variable.)
RELATED QUESTIONS

4t^2+4t+1 Factor experssion (answered by Nate)
solve t^2 + 4t =... (answered by stanbon)
4t^2+4t+1 answer is (2t=1)^2 Could you explain this equation to me. I'm... (answered by jim_thompson5910)
21)Solve the equation for x. 3/4x-1/2=-8 Type an integer or fraction. Simplify your (answered by rfer)
6(1/4t+3/8)=2 (answered by unlockmath)
how to rewrite the expression (4t)^2/3 or 4... (answered by stanbon)
Solve: (2t + 1)^3 = (2t + 1) My solution: (2t + 1)^3 / (2t + 1) = (2t + 1) / (2t +... (answered by richwmiller)
2/3+1/4t=1/3 (answered by checkley71)
2/3 +... (answered by rfer)