# help with variable multiplication and division please

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#1
I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
0
5 years ago
#2
(Original post by nhtw)
I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
Multiplying can give spurious solutions whilst dividing loses solutions (some times) precisely when so you're essentially dividing by zero.

You could also manipulate that into after which a quick sketch demonstrates no solutions.
0
5 years ago
#3
(Original post by nhtw)
I always get confused with when I am allowed to multiply or divide by variables.

I know you cant divide a variable if it can equal 0 because you will lose solutions.

So what is the rule with multiplying by a variable? please also tell me other rules that I haven't mentioned if there are any.

for example 1/cos(x)=sin(x)/cos(x)

I know that there are no solutions for this equation but my working goes

times both sides by cos(x) to get 1=sin(x) which does give solutions so what is wrong?
P.S: you're not dividing or multiplying variables, you dividing and multiplying functions.
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