Question

Quick question

Answer 1

quick would be having it in the topic \(\uparrow\)

Answer 2

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

Answer 3

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

Answer 4

I would multiply everything by \(8x\)

Answer 5

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

Answer 6

I like your style zz

Answer 7

:)

Answer 8

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

Answer 9

That works

Answer 10

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

Answer 11

\[4x - 4 - 8x/32 = 1/x\]

Answer 12

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?

Answer 13

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. :)

Answer 14

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

Answer 15

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!

Answer 16

Hehe yeah, I love that

Answer 17

Especially with partial fractions

Answer 18

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

Answer 19

word