# algebra

Solve the following rational inequality. Write the solution in interval notation. Show the number line and breaking points or graph of the polynomial with the part of the graph that is the solution (x-4)(x+2)/(x-3)(x+5) ¡Ü0

1. 👍
2. 👎
3. 👁
1. I have a strong feeling you meant
(x-4)(x+2)/( (x-3)(x+5) ) ≥ 0

I good and fast way is to look at the graph of
y = (x-4)( (x+2)/(x-3)(x+5) )

http://www.wolframalpha.com/input/?i=y+%3D+%28x-4%29%28x%2B2%29%2F%28%28x-3%29%28x%2B5%29%29

It shows the graph to be above the x-axis , ( > 0 ) , for x < -5, between -2 and 3 and then again for x > 4
However we must exclude x = 3 and x = -5, since we have vertical asymtotes at these two values

so if your symbol is to be ≥ , then

-2 ≤ x < 3 OR x ≥ 4

another way to algebraically analyse it .
The "critical " values of x are -5, -2, 3, and 4
splitting up the x-axis into 5 sections.
I will then arbitrarily pick any value in each region and calculate using only the ± signs of the factors. We don't really care what the actual answer is, we only care about whether it is + (above) or - (below)

1. for any x < -5
let x = -6, I get (-)(-)/((-)(-) > 0 , that's good
2. for -5<x<-2
let x = -4, I get (-)(-2)/((-)(+)) < 0 , no good
3. for -2 < x < 3
let x = 0 , I get (-)(+)/((-)(+)) > 0 , that's good
4. for 3 < x < 4
let x = 3.5, I get (-)(+)/((+)(+) < 0 , no good
5. for x > 4
let x = 10 , I get (+)(+)/((+)(+)) > 0 , that's good again

so we have:
x < -5 OR -2≤ x < 3 OR x ≥ 4

1. 👍
2. 👎
2. less than or equal to

1. 👍
2. 👎

## Similar Questions

1. ### Math

1. 5h – 9 = –16 + 6h (1 point) 4 –7 7 10 2. 4x + 4 = 9x – 36 (1 point) –8 –7 8 –3 3. Which of the following equations has an infinite number of solutions? (1 point) 3x – 3 = –4x 2y + 4 – y = 16 7x + 5 = 4x + 5

2. ### IMPORTANT MATH NEED HELP NOW!!!

. Evaluate the expression. 2(y + 2) for y = 3 (1 point) –4 8 10 2 2. The cost in dollars of a field trip is 64 + 14n, where n is the number of people attending. What is the cost for 48 people? (1 point) \$736 \$126 \$896 \$910 3.

3. ### Math!

Please Please Please help me! I'm really behind and need to get this done and i'm really confused. 1. 5h – 9 = –16 + 6h (1 point) 4 –7 7 10 2. 4x + 4 = 9x – 36 (1 point) –8 –7 8 –3 3. Which of the following equations

4. ### Math

Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line. 1. 2(3x + 1)< -10 or 3(2x - 4) ¡Ý 0 The or means union of these inequalities. 2. 5(p + 3) + 4 > p - 1 or 4(p - 1) +

1. ### Algebra

Write the solution set of the inequality |x + 2| < 5 in the interval notation.

2. ### Math

Solve the inequality. Expression solution set using interval notation and graph the solution set using a number line. -15x+3

3. ### Algebra 2

Write the solution to the given inequality in interval notation. [-3,-1) (-3,-1] (-∞,-3) U [-1,∞) (-∞,-3] U (-1,∞)

4. ### math

solve the compound inequality write the solution in interval notation 2u+4>-6 and 3u-6> -3

1. ### College Algebra

Graph the inequality on the number line and then write it in interval notation. 8x+5(x+5)≥2x+58 Please can you help me with the interval notation and graph number line description ( where plot the point what direction the line

2. ### algebra

solve the inequality. Express the solution using interval notation and graph the solution set on the real number line x-4/x^2-4 greater or equal to O