Mathematics. Please show me and explain this?

Question

Could you show me how to solve these and help me understand this better.

a)

x2 - 1
-----------------
x + 1


b)

5x2 – 5
-------------------
x – 1


c)

x2 + 2x + 1
----------------------
x + 1


d)

x2 – 8x + 16
----------------------
x - 4

Answer 1

You need to expand each of these to make it work. (It takes some practice to see how to expand at a glance. But since you are trying to solve a good first guess would be to try using the denominator.)

a)

(x+1)(x-1)
--------------
(x+1)

simplifies to
x-1

b)

5(x-1)(x+1)
----------------
(x-1)

simplifies to
5(x+1) or 5x+5

c)

(x+1)(x+1)
---------------
(x+1)

simplifies to
x+1

d)

(x-4)(x-4)
---------------
(x-4)

simplifies to

x-4

The trick is to see how to expand the term to enable you to simplify!

Answer 2

These cannot be solved (as they are not equations), but can be simplified.

a) (x2 - 1) / (x+1) = (x-1)(x+1)/(x+1) = x-1
[Note: a2 - b2 = (a-b)(a+b)]

b) (5x2 - 5)/(x-1) = 5(x2-1)/(x-1) = 5(x-1)(x+1)/(x-1) = 5(x+1)
[Note: take out the common factor, ie. 5]

c) (x2 + 2x + 1)/(x+1) = (x+1)(x+1)/(x+1) = x+1
[Note: factorise any quadratic equations. This requires some practise, but isn't too difficult.]

d) (x2 - 8x + 16)/(x-4) = (x-4)(x-4)/(x-4) = x-4
[Note: factorisation again.]

Answer 3

a) x2- 1/ x+1= (x+1)(x-1)/x+1= x-1

b)5x2-5/x-1= 5(x2-1)/x-1= 5(x+1)(x-1)/x-1= 5x+5

c)x2+2x+1/x+1= (x+1)(x+1)/x+1= x+1

d)x2-8x+16/ x-4= (x-4)(x-4)/ x-4= x-4


Now the teatcher will be satisfied!

Answer 4

a) x2-1/x=1
factor the top: (x-1)(x+1)/x=1
cancel the x+1
your answer is just x-1

b)5x2-5/x-1
factor: 5(x2-1)/x-1
you can keep factoring: 5(x-1)(x+1)/x-1
cancel
your answer is 5(x+1)

c)x2+2x+1/x+1
factor: (x+1)(x+1)/x+1
cancel
your answer is x+1

d)x2-8x+16/x-4
factor: (x-4)(x-4)/x-4
cancel your answer is x-4

Answer 5

(x^2 - 1)/(x +1) = (x-1)(x+1)/ (x+1) =(x-1)
(5x^2 -5)/(x -! ) = 5 (x+1)(x -1)/(x - 1) =5(x+ 1)
(x^2 +2x +1)/(x +1) = (x+1)(x+1)/(x+1) =(x+1)
(x^2 -8x +16)/(x-4) = (x -4)(x-4)/(x-4) =(x-4)

Answer 6

a)
(x - 1).(x + 1) / (x + 1) = x - 1

b)
5.(x - 1).(x + 1) / (x - 1) = 5.(x + 1)

c)
(x + 1).(x + 1) / (x + 1) = x + 1

d)
(x - 4).(x - 4) / (x - 4) = x - 4

Answer 7

Problem A contains a difference of squares in the numerator... That is the numerator can be factored like this...
(x+1)(x-1)
-------------
x+1

Since the numerator and denominator contain (x+1) you can cancel and reduce to get (x-1)

If you have difficulty factoring use my factoring calculator at http://www.poodwaddle.com/mathfactor.html
Let me know if you like it and if there are any other calculators you might find useful.

Answer 8

a)

x² - 1
------- =
x + 1
Factoring and cancelling:
(x+1)(x-1)
------------ = x-1
x+1
><
b)

5x² – 5
--------- =
x – 1

5(x² - 1)
---------- =
x -1
Factoring and cancelling:
5(x+1)(x-1)
-------------- = 5(x+1)
x-1
><
c)
x² + 2x + 1
----------------------
x + 1
Factoring and cancelling:
(x+1)(x+1)
------------- = x+1
x+1
><
d)
x² – 8x + 16
---------------- =
x - 4
Factoring and cancelling:
(x-4)(x-4)
------------- = x-4
x-4
><