## Compassionate one year ago Quick question

1. zzr0ck3r

quick would be having it in the topic $$\uparrow$$

2. Compassionate

$\frac{1}{x} = \frac{x - 1}8 - \frac{x}{4}$ My first step would be $\frac{x-1}{8} - \frac{x \times 2}{4 \times 2}$

3. Compassionate

Didn't want to put more than one line of LaTeX in the subject and make it freeze up on me.

4. zzr0ck3r

I would multiply everything by $$8x$$

5. Astrophysics

$\huge \frac{ a }{ b } \pm \frac{ c }{ d } \implies \frac{ ad \pm bc }{ bd }$ pretty much with all fractions

6. Astrophysics

7. zzr0ck3r

:)

8. Compassionate

$\frac{4(x - 1) - 8x}{32}$

9. Astrophysics

That works

10. Astrophysics

You can now cross multiply with the left side if you like

11. Compassionate

$4x - 4 - 8x/32 = 1/x$

12. Compassionate

I get it. So when adding or subtracting, we can use the ab + bd/ad rule, and when multiplying, we can cross multiply, and when dividing we can take the recipricol?

13. Astrophysics

Yeah sort of, but know what kind of algebraic rules are going on, when we cross multiply for example we're just multiplying both sides by 32 and x, so yes reciprocal. :)

14. Astrophysics

I mean this rule isn't anything special, it's just as you would do fractions regularly, finding common denominator..etc

15. zzr0ck3r

In general it is a good idea to learn the following trick $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{c}\\ abc\dfrac{1}{a}+abc\dfrac{1}{b}=abc\dfrac{1}{c}\\ bc+ac=ab$ When we have fractions, it is easy to clear the denominators when we have an equals sign!

16. Astrophysics

Hehe yeah, I love that

17. Astrophysics

Especially with partial fractions

18. Compassionate

Yes. Clearing fractions. I understand. I'm just brushing up on my skills.

19. zzr0ck3r

word