# Show that one equation equals another (simple algebra)

I have what appears to be a simple question but am lost as how to start it. I have been asked to show that:

$$\left|\frac{64}{3x-5}-4\right|=\left|\frac{12}{3x-5}\right|\cdot|x-7|$$

Is there some sort of logical process that I can follow in this instance - a process I could put into code for a computer to follow, or do I simply need to have some sort of insight to 'see' what I need to do, because that is something I am really bad at.

Could someone please instruct me on how I should start this, and also let me know what the significance of the absolute brackets are? I find them confusing and don't understand their purpose in this question.

Thank you

• It would definitely help if you knew about some of the properties of the absolute brackets i.e. |(x+3)(x+2)|=|x+3||x+2|, but other than that all you had to do was find a common denominator, factor the top and use the property I gave you above. – RonaldB Aug 3 '16 at 7:03

• @user88720 I used the following: Suppose we have $\frac{a}{b}-c$, then we can write it as $\frac{a}{b}-\frac{cb}{b}=\frac{a-cb}{b}$. Apply this with $a=64$, $b=3x-5$, and $c=4$. – Karthik Aug 3 '16 at 7:13