explain how subtraction of rational expressions is used in photography, homework help

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to explain how subtraction of rational expressions is used in photography. Include an equation that could be used to find the distance between the lens and the film if the focal length of the lens is 50 millimeters and the distance between the lens and the object is 1000 millimeters.

8-2
Adding and Subtracting
Rational Expressions
Main Ideas
• Determine the LCM of
polynomials.
• Add and subtract
rational expressions
GET READY for the Lesson
In order to produce a picture that is “in focus,” the distance
between the camera lens and the film q must be controlled so that
it satisfies a particular
relationship. If the
distance from the
subject to the lens
is p and the focal
length of the lens
is f, then the
formula 1 – –
can be used to
determine the
correct distance
between the lens
object
image on film
and the film
LCM of Polynomials To find or- , you must first find the least
common denominator (LCD). The LCD is the least common multiple
(LCM) of the denominators.
To find the LCM of two or more numbers or polynomials, factor each
number or polynomial. The LCM contains each factor the greatest
number of times it appears as a factor.
LCM of a? – 6a +9 and a? +a – 12
6 = 2.3
42-64 + 9 = (a – 3)2
4 = 22
2? + – 12 = (a – 3)(a + 4)
LCM = 22.3 or 12 LCM = (a – 3)2 + 4)
LCM of 6 and 4
Factor the second monomial
Factor the third monomial
EXAMPLELCM of Monomials
Find the LCM of 18r+s”, 24rºst, and 15st.
18r2,5 – 2.32.2.55 Factor the first monomial
24rºst? = 23.3.8.5.2
15st = 3.5.33.1
LCM = 2.3.5.v.5.2 Use each factor the greatest number of times
= 360rs42
it appears as a factor and simplity
JOHECZYour Progress
Find the LCM of each set of monomials.
1A. 1244, 27ac”, 18ab2c 1B. 6mnº, 42mnp2, 36mºny
450 Chapter 8 Rational Expressions and Fuations