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Mathematics 10 Online
OpenStudy (anonymous):

pls.......answer the 25th question

OpenStudy (anonymous):

OpenStudy (anonymous):

pls.......HELP..

OpenStudy (amistre64):

do you know how to add and subtract fractions?

OpenStudy (anonymous):

yes\

OpenStudy (amistre64):

that is all the first option is doing; it just looks messy

OpenStudy (anonymous):

its looking too messy 4 me .help

OpenStudy (amistre64):

\[\frac{m+n}{p+q}-\frac{m-n}{p-q}\] \[\frac{(m+n)(p-q)}{(p+q)(p-q)}-\frac{(p+q)(m-n)}{(p+q)(p-q)}\] \[\frac{(m+n)(p-q)-(p+q)(m-n)}{(p+q)(p-q)}\]

OpenStudy (amistre64):

\[\frac{(m+n)(p-q)-(p+q)(m-n)}{(p+q)(p-q)}\] \[\frac{mp-nq+np-mq-mp-mq+np+nq}{p^2-q^2}\] \[\frac{\cancel{mp}\cancel{-nq}+np-mq\cancel{-mp}-mq+np\cancel{+nq}}{p^2-q^2}\] \[\frac{2np-2mq}{p^2-q^2}\] \[\frac{2(np-mq)}{p^2-q^2}\]

mathslover (mathslover):

@amistre64 it is being shown to me : Math Processing Error] [Math Processing Error] [Math Processing Error] [Math Processing Error] [Math Processing Error]

OpenStudy (amistre64):

mathslover, try doing a hard caache reset: Ctrl+f5

mathslover (mathslover):

OK, let me try

OpenStudy (amistre64):

otherwise, its prolly just telling you that i messed it up big time :)

mathslover (mathslover):

:) , it is working now, sorry for interrupting and must say "excellent work sir"

OpenStudy (amistre64):

yay!!

OpenStudy (anonymous):

\[\frac{7+3\sqrt{5}}{3+\sqrt{5}}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}=a+\sqrt{5}b\] \[\frac{(7+3\sqrt{5})(3-\sqrt{5})-(7-3\sqrt{5})(3+\sqrt{5})}{(3+\sqrt{5})(3-\sqrt{5})}=a+\sqrt{5}b\] \[\frac{(21-7\sqrt{5}+9-15)-(21+7\sqrt{5}-9-15)}{3^{2}-(\sqrt{5})^{2}}=a+\sqrt{5}b\] \[\frac{(15-7\sqrt{5})-(-3+7\sqrt{5})}{9-5}=a+\sqrt{5}b\] \[\frac{(15-7\sqrt{5})-(-3+7\sqrt{5})}{4}=a+\sqrt{5}b\] \[\frac{15-7\sqrt{5}+3-7\sqrt{5}}{4}=a+\sqrt{5}b\] \[\frac{18-14\sqrt{5}}{4}=a+\sqrt{5}b\] \[\frac{9-7\sqrt{5}}{2}=a+\sqrt{5}b\] \[\frac{9}{2}-\frac{7\sqrt{5}}{2}=a+\sqrt{5}b\] Now comparing LHS and RHS, \[a=\frac{9}{2}\] and \[\sqrt{5}b=\frac{-7\sqrt{5}}{2}\] \[b=\frac{-7}{2}\]

mathslover (mathslover):

lol , direct solution ;)

OpenStudy (anonymous):

isn't,.....\[3\sqrt{5}\times3=9\sqrt{5}\]

OpenStudy (amistre64):

that it is

OpenStudy (amistre64):

using m=7 n=3sqrt(5) p=3 q=sqrt(5) \[\frac{2(np-mq)}{p^2-q^2}\] \[\frac{2((3)3\sqrt{5}-7\sqrt{5})}{3^2-\sqrt{5}^2}\] \[\frac{2(9\sqrt{5}-7\sqrt{5})}{9-5}\] \[\frac{2(2\sqrt{5})}{4}=\sqrt{5}\] so i might be wrong ....

OpenStudy (anonymous):

wat?

OpenStudy (amistre64):

youll have to be more concise as to what your confusion may be ...

OpenStudy (anonymous):

in @shubham.bagrecha 's answer 3sqrt5 x 5 is wrong @amistre64

OpenStudy (amistre64):

i agree that shub has a few typos :) i like mine better, its much cleaner to read thru

OpenStudy (amistre64):

looks like 0 + sqrt(5)*1 is a good answer tho

OpenStudy (anonymous):

but how do we get the answer.... @amistre64

OpenStudy (amistre64):

in my method, a generalized the values into variable; and worked thru the structure to simplify the form then i inserted the specific values into their proper place holders to determine the solution

OpenStudy (anonymous):

but u gt the ansr sqrt5 ....nt 0+sqrt5x1

OpenStudy (anonymous):

is there any difference btw. the two?@basith

OpenStudy (amistre64):

yes, which means that by comparison to: a + sqrt(5) b ; that a=0 and b=1

OpenStudy (anonymous):

cn u hlp me with the 2nd part too... :)

OpenStudy (amistre64):

do you understand the first part?

OpenStudy (anonymous):

yes......thnx 4 tht :)

OpenStudy (amistre64):

then how can we use the knowledge from that to work out a suitable result for the second part?

OpenStudy (amistre64):

first, generalize with variables\[\frac{a}{p-q}\] then work thru the structure to conform it to what they are asklng for ... how do we rationalize a denominator?

OpenStudy (anonymous):

pls.....wait a min

OpenStudy (anonymous):

\[\frac{ 25\sqrt{40}+25\sqrt{80} }{ -40 }\] then wat

OpenStudy (amistre64):

then you can unravel the sqrts. they have perfect square factors that can be pulled out to conform them to: x sqrt(5) and ysqrt(10)

OpenStudy (anonymous):

is it 7.905

OpenStudy (anonymous):

@amistre64

OpenStudy (amistre64):

im getting -9.xxxx

OpenStudy (amistre64):

notice that you have a negative on the bottom, and a positive value up top; regardless of what the specifics are; the answer will have to be negative

OpenStudy (amistre64):

the rest of it is just keeping track of your operations

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