hectictar

\(f(x)=\dfrac{2x-3}{x+1}\\~\\ f(3a-2)=\dfrac{2(3a-2)-3}{(3a-2)+1}\\~\\ \ \\~\\ f(3a-2)\ =\ 1\\~\\ \dfrac{2(3a-2)-3}{(3a-2)+1}\ =\ 1\\~\\ \ \\~\\ \dfrac{6a-4-3}{3a-2+1}\ =\ 1\\~\\ \dfrac{6a-7}{3a-1}\ =\ 1\\~\\ \begin{array}{} 6a-7\ =\ 1(3a-1)&\qquad\text{and}\quad3a-1\neq0\\~\\ 6a-7\ =\ 3a-1&\qquad\text{and}\quad3a-1\neq0\\~\\ 6a-3a\ =\ 7-1&\qquad\text{and}\quad3a-1\neq0\\~\\ 3a\ =\ 6&\qquad\text{and}\quad3a-1\neq0\\~\\ a\ =\ 2&\qquad\text{and}\quad a\neq\frac13 \end{array}\\~\\ a\ =\ 2 \)

\(f(x)\ =\ g(x+1)-g(x-1)\\~\\ \color{purple}{f(\frac12)}\ =\ g(\frac12+1)-g(\frac12-1)\\~\\ \color{purple}\phantom{f(\frac12)}\ =\ g(\frac32)-g(-\frac12)\\~\\ \color{purple}\phantom{f(\frac12)}\ =\ 1--1\\~\\ \color{purple}\phantom{f(\frac12)}\ =\ 2\\~\\ \color{Green}{f(-\frac12)}\ =\ g(-\frac12+1)-g(-\frac12-1)\\~\\ \color{Green}\phantom{f(\frac-12)}\ =\ g(\frac12)-g(-\frac32)\\~\\ \color{Green}\phantom{f(\frac-12)}\ =\ 1--1\\~\\ \color{Green}\phantom{f(\frac-12)}\ =\ 2\\~\\ f(\frac12)+f(-\frac12)\ =\ 2+2\ =\ 4\)

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60 hours   =   48 hours  +  12 hours

Total pay for the week   =   $17.25 * 48   +   1.5 * $17.25 * 12   =   $1138.50

It looks like just making a box with the \hspace command makes a narrower box like this:

\(\boxed{\hspace{10cm}}\)

And I tried to use the \vspace command to make it taller but it seems like that doesn't work in math mode :\

Another code I like to use to make things invisible is  \phantom{}

It will makes whatever you put inside invisible! I sometimes use it for spacing

Also there is the  \hspace  command which can be used to make a horizontal space of a specified length.

For example, the code:  a\hspace{3cm}b

makes this:

\(a\hspace{3cm}b\)

So there are 3 cm of space between the a and the b.

Couldn't have said it any better! :)

a*b  =  2a - b²

a*6  =  2a - 6²  =  8

2a - 6²  =  8

2a - 36  =  8

2a  =  44

a   =   22

1  =  3x - 8

9  =  3x

3  =  x

s(t(3))  =  3² + 8(3) - 2

s(  1  )  =  9 + 24 - 2

s(  1  )  =  31

Since △ABC ~ △ACD,

AC / AD   =   AB / AC

AC / AD  =  AB / AC

x / 12  =  27 / x

x * x / 12   =   27

x * x   =   27 * 12

x²   =   324

x   =   sqrt(324)

x   =   18

a/c   =   a/b * b/c

\(\frac{a}{c}\ =\ \frac{a}{b}\cdot\frac{b}{c}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt{10}}{\sqrt{21}}\cdot\frac{\sqrt{14}}{\sqrt{15}}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt{10\ \cdot\ 14}}{\sqrt{21\ \cdot\ 15}}\\~\\ \frac{a}{c}\ =\ \sqrt{\frac{10\ \cdot\ 14}{21\ \cdot\ 15}}\\~\\ \frac{a}{c}\ =\ \sqrt{\frac49}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt4}{\sqrt9}\\~\\ \frac{a}{c}\ =\ \frac23\)

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