x/x – 1 - 3/x = 1/4
My problem says to show the work and to solve the equation. I am not sure how to use the steps to show my work and answer the problem.
Thanks.
To solve the given equation x/x - 1 - 3/x = 1/4, you can follow these steps:
Step 1: Simplify the fractions:
- The fraction x/x simplifies to 1, since any number divided by itself equals 1.
- Rewrite the equation as 1 - 1 - 3/x = 1/4.
Step 2: Combine similar terms:
- Simplify the left side of the equation: 1 - 1 is equal to 0. Rewrite the equation as -3/x = 1/4.
Step 3: Cross multiply:
- Cross multiply by multiplying the numerator of one fraction by the denominator of the other fraction.
- Multiply -3 by 4 and x by 1 (since 1 is the denominator of the fraction 1/4). This gives us -12 = x.
Step 4: Solve for x:
- The equation -12 = x means x is equal to -12.
So, the solution to the equation x/x - 1 - 3/x = 1/4 is x = -12.
To show your work, you can write down the steps as mentioned above, starting with the original equation and proceeding with the simplifications, combining like terms, cross multiplying, and finally solving for x.