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2 years ago

Simplify the expression below.

Mathematics

1 answer:

vitfil [10]2 years ago

6 0

Answer:

y^2/4x^4

Step-by-step explanation:

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HELP ASAP!!

garri49 [273]

I'm pretty sure it would be x - y + 1 = 0 because if you plug in one of the coordinates into each equation, this is the only one that works.

y - x + 1 = 0
2 - 1 + 1 = 0
2 = 0 not correct

x - y + 1 = 0
1 - 2 + 1 = 0
0 = 0 correct

-x - y + 1 = 0
-1 - 2 + 1 = 0
-2 = 0 not correct

4 0

3 years ago

Two problems here I need solved! I need every step, so please have that with your answers!!

Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x(x-4) - 2(x - 4)}.$

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{(x-4)(x - 2)}$

We multiply through by LCM of
$(x-4)(x - 2)$

$(x - 2) + x(x-4) = 2$

We expand to get,

$x - 2 + {x}^{2} - 4x= 2$

We group like terms and equate everything to zero,

${x}^{2} + x - 4x - 2 - 2 = 0$

We split the middle term,

${x}^{2} + - 3x - 4 = 0$

We factor to get,

${x}^{2} + x - 4x- 4 = 0$

$x(x + 1) - 4(x + 1) = 0$

$(x + 1)(x - 4) = 0$

$x + 1 = 0 \: or \: x - 4 = 0$

$x = - 1 \: or \: x = 4$

But
$x = 4$
is not in the domain of the given equation.

It is an extraneous solution.

$\therefore \: x = - 1$
is the only solution.

QUESTION 2

$\sqrt{x+11} -x=-1$

We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

$x + 11 = (x - 1)^{2}$

We expand to get,

$x + 11 = {x}^{2} - 2x + 1$

This implies,

${x}^{2} - 3x - 10 = 0$

We solve this quadratic equation by factorization,

${x}^{2} - 5x + 2x - 10 = 0$

$x(x - 5) + 2(x - 5) = 0$

$(x + 2)(x - 5) = 0$

$x + 2 = 0 \: or \: x - 5 = 0$

$x = - 2 \: or \: x = 5$

But
$x = - 2$
is an extraneous solution

$\therefore \: x = 5$

7 0

3 years ago

Evaluate the piecewise function below for f(3):

gregori [183]

F(3)={2(3)-9}
F(3)={6-9}
F(3)={-3}

8 0

3 years ago

Please answer quickly thanks

Anastaziya [24]

8/3 = 2 2/3 and -11/3 = -3 2/3
so the middle line is 0 and each big line is 1.
Put the first dot on 2 2/3 or right before the 3rd big line.
Put the second dot on -3 2/3 or the line right after the 4th big line going back from 0

3 0

3 years ago

A group of 9 friends went bowling. Each person pays the same amount to bowl several games and a $3 fee to rent

ruslelena [56]

Answer: Each friend would pay $15.

3 0

3 years ago

Read 2 more answers