If [(x-1)/(x+1)] + [(x+1)/(x-1)] is written as mixed number A B/C, then B=______
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
You should write `(x-1)/(x+1) + (x+1)/(x-1)` as a mixed number that consists in a combination of a whole number and a proper fraction, such that:
`(x-1)/(x+1) + (x+1)/(x-1) = ((x-1)(x-1) + (x+1)(x+1))/((x-1)(x+1))`
`(x-1)/(x+1) + (x+1)/(x-1)= ((x-1)^2 + (x+1)^1)/(x^2-1)`
Expanding the binomials to numerator yields:
`(x-1)/(x+1) + (x+1)/(x-1) = (x^2-2x+1+x^2+2x+1)/(x^2-1)`
`(x-1)/(x+1) + (x+1)/(x-1) = (2x^2+2)/(x^2-1)`
Factoring out 2 yields:
`(x-1)/(x+1) + (x+1)/(x-1) = 2(x^2+1)/(x^2-1)`
Hence, since the result is a mixed number, you may identify the whole number as `A = 2` , the numerator of the fraction `B = x^2+1` and the denominator `C = x^2-1` .
Hence, converting the given expression in a mixed number yields that `B = x^2+1.`
Related Questions
- Given that `f(x)` is a function which of the following statements are true:i If `f` is continuous...
- 1 Educator Answer
- If a^2+b^2+c^2 = 1 and a^3+b^3+c^3 = 1 then what is the value of a+b+c.
- 2 Educator Answers
- if a^x=b^y=c^z and b^2=ac Prove that, 1/x+1/z=2/y.
- 1 Educator Answer
- if x=a(y+z), y= b(z+x) & z= c(x+y) then, prove that, ab+bc+ca+2abc=1. no
- 1 Educator Answer
- Using properties of determinant prove that `|[1, a, a^2],[1, b, b^2],[1, c, c^2]| = (a-b)(b-c)(c-a)`
- 1 Educator Answer
For fraction:
a/b + b/a = 2 + [(b-a)^2]/ab
b=x+1
a=x-1
Then b-a = x+1 -x+1=2 and 2^2 = 4
the answer = 2 + 4/[(x+1)(x-1)] = A B/C
=> B =4
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers