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xenn [34]
3 years ago
5

(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression

Mathematics
1 answer:
DanielleElmas [232]3 years ago
4 0
Simplify the following:
((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6))

The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1):
((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6))

The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6):
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6))

x - 5 x = -4 x:
((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6))

Factor -2 out of -4 x - 6:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25))

x^2 - 25 = x^2 - 5^2:
((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3))

Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5):
((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3))

((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)):
((x - 6) (x + 1))/(-2 (2 x + 3))

Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:

Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
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3 years ago
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ivolga24 [154]

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3 years ago
find the area of a parallelogram if a base and corresponding altitude have the indicated lengths base 1 1/2 feet , altitude 6 in
Ostrovityanka [42]

The area of parallelogram is 108 square inches

<em><u>Solution:</u></em>

<em><u>The formula for area of parallelogram is:</u></em>

Area = base \times height

From given,

Base = 1\frac{1}{2}\ feet = \frac{2 \times 1 + 1}{2} = \frac{3}{2}\ feet

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3 years ago
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gizmo_the_mogwai [7]

Answer:

13.

Let us say

first angle be = 4x -10

second angle = x

now add them to 90 as complementary angles add up to 90

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5x - 10 = 90

5x = 90+10

5x = 100

x = 100/5

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the first angle = 4x -10

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the second angle = x

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the angles are 70 and 20

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lana66690 [7]
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