Solve. 1/x-1 + 1/4x-4=5/4

Question

johnweldon1993 · Answer

$$\large \frac{1}{x - 1} + \frac{1}{4x - 4} = \frac{5}{4}$$

like that?

anonymous · Answer

Yes

johnweldon1993 · Answer

Notice how if you multiply the left-most fraction by 4/4   you will receive the same denominator as the right fraction.

$$\large \frac{1}{x-1} \times \frac{4}{4} = \frac{4}{4x - 4}$$   
right?

So now you have

$$\large \frac{4}{4x- 4} + \frac{1}{4x - 4} = \frac{5}{4}$$

What can you do from here?

johnweldon1993 · Answer

We can combine from fractions over the common denominator

$$\large \frac{4}{4x - 4} + \frac{1}{4x - 4} \rightarrow \frac{4 + 1}{4x - 4}$$

So now we have

$$\large \frac{5}{4x - 4} = \frac{5}{4}$$

And we can then solve for 'x'

anonymous · Answer

How do we solve for x with this problem?

johnweldon1993 · Answer

Well we can do it a long way...or a quick way...

The quick way would be...to notice that we already have the 5 on top like we want...

So we need to make the bottom become the 4 that we want...

The bottom is 4x - 4       and we want that to = 4...

so lets solve

4x - 4 = 4

anonymous · Answer

ok