Ask question

Ask question

All categories

4 years ago

11

How to solve rational equation:

1 answer:

Zina [86]4 years ago

8 0

Like when adding/subtracting fractions at any other time, you need a common denominator, in this case (x-1)(x+1)=x^2-1 so:

(2(x+1)+3(x-1))/(x^2-1)=4 multiply both sides by (x^2-1)

2x+2+3x-3=4x^2-4 combine like terms on left

5x-1=4x^2-4 subtract (5x-1) from both sides

4x^2-5x-3=0 using the quadratic formula for expediency

x=(5±√73)/8

x≈-0.443 and 1.693

You might be interested in

Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v

olga_2 [115]

We are given

$f=z^3 -x^2y$

Firstly, we can find gradient

so, we will find partial derivatives

$f_x=0 -2xy$

$f_x=-2xy$

$f_y=0 -x^2$

$f_y=-x^2$

$f_z=3z^2$

now, we can plug point (-5,5,2)

$f_x=-2*-5*5=50$

$f_y=-(-5)^2=-25$

$f_z=3(2)^2=12$

so, gradient will be

$gradf=(50,-25,12)$

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

$|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}$

$|v|=\sqrt{29}$

now, we can find unit vector

$v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

now, we can find dot product to find direction of the vector

$dir=(gradf) \cdot (v')$

now, we can plug values

$dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

$dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })$

$dir=-\frac{248\sqrt{29}}{29}$ .............Answer

7 0

4 years ago

Read 2 more answers

Complete the table for the given rule.<br> Rule: y = x-5

Tomtit [17]

Answer:

Idk hehe lol

Step-by-step explanation:

8 0

3 years ago

Erik is performing a marble experiment in math class. His teacher places an equal number of black, red, and white marbles in a b

olganol [36]

Answer:

1/3

Step-by-step explanation:

5 0

3 years ago

At most, Keith can spend $90 on sandwiches and chips for a company lunch. He already bought chips for $15 and will buy sandwiche

Vesna [10]

A. 12 sandwiches. He can buy 12 because 6*12=72. He already has the chips at 15.00. So 72+15=87. Close to the amount of $90.00

7 0

3 years ago

An angle measures 150° more than the measure of its supplementary angle. What is the measure of each angle?

madreJ [45]

Answer:

<h2> 165° and 15°</h2>

Step-by-step explanation:

x - an angle

x - 150° - the angle's suplementary angle

Measure of suplementery angles adds to 180°

x + x - 150° = 180°

2x = 180° + 150°

2x = 330°

x = 330°÷2

x = 165°

x-150° = 165° = 150° = 15°

3 0

3 years ago