URGENT: Need Maths Help

Posted:
edited January 2014
I have to hand this in on Monday, and I just can't seem to get it. The Question is solve the equation for x. I am told to keep my answers in their simplest surd form. Please ignore the dots inbetween terms, i had to do this to get the formatting right

s-5 . 1

--- + - = 0

s+1 . s

I have got this far. step1

(s-5)(s)...(1)(s+1)

--- .. - + - ------ .... =0

(s+1)(s)...(s)(s+1)

step2

s^2 -5s+s+1

----------- =0

s^2 +s

step3

s^2 -4s+1

--------- =0

s^2 +s

because the numerator of step 3 is a quadratic, i put it into the quadratic formula, but Im not sure if I should cancel out the like terms of the fraction.

step4

s= 4 +/- sqrt of 4^2 -4*1*1

------------------------

2x1

which simplifies to

s= 4 +/- sqrt of 12

----------------

2

which simplifies to 2 +/- sqrt of 12

sqrt of 12 simplifies to 2 x sqrt3

so s= 2 + 2sqrt3 or

2 - 2sqrt3.

Whats bugging me is that I almost know the answer is wrong, but I dont know why. I'm sure Im supposed to cancel out the fractions after step 3, but then I dont get the kind of answer the question is telling me to submit.

BTW, i worked out the answer in Mathcad, and its like 3.732.

Please! Im not trying to cheat, I just want to know where Im going wrong.Thankyou

Posts: 938member
You almost had it, here is the way to do it:

(s-5)/(s+1) + 1/s = 0

First rearrange:

(s-5)/(s+1) = -1/s

Multiply each numerator by the opposite denominator:

s^2 - 5s = -s - 1

Rearrange:

s^2 - 4s + 1 = 0

x = (4 +/- sqrt(16 - 4))/ 2

As the equation is quadratic it can contain as many as 2 zeros, in this case it does have 2. The solutions are:

3.7320508076 (what you found in MathCad)

and

0.2679491924

The mistake you made was here:

so s= 2 + 2sqrt3 or

2 - 2sqrt3.

You divided the 4 by 2, but you forgot to divide the term in front of the sqrt by two. The above should be:

so s= 2 + sqrt3 or

2 - sqrt3

which is the same as the answer above, in another form.
Posts: 4,442member
Many^99 thanks rick,

Ive almost got it, but im calculating 2-sqrt3 as 0.2679, i think this is what you meant, it looks like you just put the sqrt of 3?

A question. When I have cross multiplied s-5/s-1 = -1/s, to get s^2-4s+1, I still have the denominator of s^2-s. Was I right to just ignore this? I dont understand why! If you use real number fractions, you still have to divide by the product of the denominators to get an equivalent number of the original fraction? ie

(10/5)+(6/7) = (70+30)/(5*7) = (100/35) = 2.857....

Thanks again

BTW, are you familiar with MathCAD? I can only get one answer out of it at a time in a solve block. I have to tell it the range of values i believe s will be in, which is OK, when I know them, but what if I don't. Can I tell it to give me both answers?
Posts: 938member
You are right, I made a mistake as well. I forgot to subtract the second answer from 2. I fixed my original post.

You don't need to cross multiply - you are multipying both sides by the denominators. They cancel out on the same side. Example:

(s-5)/(s+1) = -1/s

multiply both sides by s:

s(s-5)/(s+1) = s(-1/s)

On the right hand side the s's cancel out so you have:

(s^2 - 5s)/(s+1) = -1

As far as MathCad is concerned, I don't know anything about it.