Solving the Equation: 1/x - 1 - 1/x + 5 = 6/7
In this article, we will solve the equation 1/x - 1 - 1/x + 5 = 6/7. This equation involves fractions and algebraic manipulation, which can be challenging to solve. But don't worry, we'll break it down step by step.
Step 1: Combine like terms
Let's start by combining the fractions that have the same denominator (x):
1/x - 1/x = (1 - 1)/x = 0/x = 0
So, the equation becomes:
-1 + 5 = 6/7
Step 2: Simplify the equation
Next, let's simplify the equation by combining the constants:
4 = 6/7
Step 3: Cross-multiply
Now, let's cross-multiply to eliminate the fraction:
4 × 7 = 6 × 1
Step 4: Solve for the equation
Finally, let's solve for the equation:
28 = 6
Conclusion
Unfortunately, the equation 1/x - 1 - 1/x + 5 = 6/7 does not have a solution, as we ended up with a contradictory equation (28 = 6). This means that there is no value of x that satisfies the equation.
