Question
Asked Oct 27, 2019

I need help working this problem. I get stuck at this point. I think my algebra is failing with the double division. Thank you for any help.

2 Find the average rate of change of mt)- 2
between tex and t xth. Simplify
of ch
2
(xth)
(x)-
(xth)-x
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2 Find the average rate of change of mt)- 2 between tex and t xth. Simplify of ch 2 (xth) (x)- (xth)-x

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Expert Answer

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Step 1

Given function: m(t)=2/(t-1)

f(b)-f(a)
Average rate of change for f(x) as x varies from a tobis given as
b-а
In the given question, a=x; b=x +h
Substitute in the given formula
2
(х+h)-1 (х)-1
(xh)x
Average rate of change =
2
2
(х+h)-1 (х)-1
h
- लाच कन)
2
2
(х+h)-1 (х)-1
h
help_outline

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f(b)-f(a) Average rate of change for f(x) as x varies from a tobis given as b-а In the given question, a=x; b=x +h Substitute in the given formula 2 (х+h)-1 (х)-1 (xh)x Average rate of change = 2 2 (х+h)-1 (х)-1 h - लाच कन) 2 2 (х+h)-1 (х)-1 h

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Step 2

Mulitply and divide the expression by (x+h-1)(x-1);

(х+h-1) (х-1)
(х+h-1) (х-1)
1
2
_
=
n (x+h)-1 (х)-1
Split the terms;
(XH1(x-)
hxh (x+h-1)(x-1)
(x+h-1) -)
4 (x+h-1)(x-1)
1
2
1
2
h
2 (х -1)
h (x+h-1)(х-1)
2(x+h-1)
h (x+h-1)(х-1)
1
1
help_outline

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(х+h-1) (х-1) (х+h-1) (х-1) 1 2 _ = n (x+h)-1 (х)-1 Split the terms; (XH1(x-) hxh (x+h-1)(x-1) (x+h-1) -) 4 (x+h-1)(x-1) 1 2 1 2 h 2 (х -1) h (x+h-1)(х-1) 2(x+h-1) h (x+h-1)(х-1) 1 1

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Step 3

Since common denominator has been ow obtained, the ter...

2(х-1)- 2(х+h-1
(х +h-1)(х-1)
h
21-28 -2К
(х+h-1)(х-1)
-2
(х+h-1)(х-1),
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2(х-1)- 2(х+h-1 (х +h-1)(х-1) h 21-28 -2К (х+h-1)(х-1) -2 (х+h-1)(х-1),

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