Ask question

Ask question

All categories

Elena-2011 [213]

3 years ago

13

Solve it using quadratic formula.grade 910 points

1 answer:

madreJ [45]3 years ago

5 0

Answer:

{-1/4, 1}
{3/4, 6}

Step-by-step explanation:

1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.

$\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}$

__

2. Using the same idea here, we get ...

$\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}$

You might be interested in

What is the range of the function y=3/x+8?

myrzilka [38]

The domain of the function is (-∞, -8) and (-8, ∞). Then the range of the function will be (-∞, 0) and (0, ∞).

<h3>What are domain and range?</h3>

The domain means all the possible values of the x and the range means all the possible values of the y.

The function is given below.

y = 3/(x + 8)

Then the domain of the function is (-∞, -8) and (-8, ∞). Then the range of the function will be (-∞, 0) and (0, ∞).

More about the domain and range link is given below.

brainly.com/question/12208715

#SPJ1

3 0

2 years ago

Which of the following describes an angle with a vertex at Z?

Tresset [83]

B is the answer and why is bc I took the quiz

5 0

3 years ago

The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the rati

Ksivusya [100]

<h2>Answer:</h2>

The ratio of the area of region R to the area of region S is:

$\dfrac{24}{25}$

<h2>Step-by-step explanation:</h2>

The sides of R are in the ratio : 2:3

Let the length of R be: 2x

and the width of R be: 3x

i.e. The perimeter of R is given by:

$Perimeter\ of\ R=2(2x+3x)$

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:

$Perimeter=2(L+B)$ )

Hence, we get:

$Perimeter\ of\ R=2(5x)$

i.e.

$Perimeter\ of\ R=10x$

Also, let " s " denote the side of the square region.

We know that the perimeter of a square with side " s " is given by:

$\text{Perimeter\ of\ square}=4s$

Now, it is given that:

The perimeters of square region S and rectangular region R are equal.

i.e.

$4s=10x\\\\i.e.\\\\s=\dfrac{10x}{4}\\\\s=\dfrac{5x}{2}$

Now, we know that the area of a square is given by:

$\text{Area\ of\ square}=s^2$

and

$\text{Area\ of\ Rectangle}=L\times B$

Hence, we get:

$\text{Area\ of\ square}=(\dfrac{5x}{2})^2=\dfrac{25x^2}{4}$

and

$\text{Area\ of\ Rectangle}=2x\times 3x$

i.e.

$\text{Area\ of\ Rectangle}=6x^2$

Hence,

Ratio of the area of region R to the area of region S is:

$=\dfrac{6x^2}{\dfrac{25x^2}{4}}\\\\=\dfrac{6x^2\times 4}{25x^2}\\\\=\dfrac{24}{25}$

6 0

3 years ago

Read 2 more answers

Tell whether this statement is sometimes, always, or never true. Identify the answer with a sketch. If B is a point between A an

Ksivusya [100]

The statement is always true

7 0

3 years ago

The lenght of a rectangle is 27 cm and its width is 15 cm. *

valentina_108 [34]

Answer:

Ok

Step-by-step explanation:

So should I find area or perimeter?

5 0

3 years ago

Read 2 more answers