Mathematics, 28.03.2020 22:42 100154281

A student solves the following equation and
determines that the solution is -2. Is the student
correct? Explain.
3/a+2 - 6a/a^2-4 = 1/a-2

Answers: 3

Show answers

Answers

Answer from: Birlem101

Solving the equation, it is found that it has no solutions, thus, the student is not correct.

The equation is:

$\frac{3}{a + 2} - \frac{6a}{a^2 - 4} = \frac{1}{a - 2}$

Applying the subtraction of perfect squares, we have that:

a^2 - 4 = (a - 2)(a + 2)

Then

$\frac{3}{a + 2} - \frac{6a}{(a - 2)(a + 2)} = \frac{1}{a - 2}$

$\frac{3}{a + 2} - \frac{6a}{(a - 2)(a + 2)} - \frac{1}{a - 2} = 0$

$\frac{3(a - 2) - 6a - (a + 2)}{(a - 2)(a + 2)} = 0$

$\frac{3a - 6 - 6a - a - 2}{(a - 2)(a + 2)} = 0$

$\frac{-4a - 8}{(a - 2)(a + 2)} = 0$

In a fraction, the denominator cannot be zero, thus:

$a - 2 \neq 0 \rightarrow a \neq 2$

$a + 2 \neq 0 \rightarrow a \neq -2$

Looking at the numerator for the solution:

-4a - 8 = 0

4a = -8

$a = -\frac{8}{4}$

a = -2

However, a = -2 is a restriction, as it makes the denominator zero, thus the function has no solutions.

A similar problem is given at link

Answer from: dakotagorski05

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

Step-by-step explanation:

Considering the expression

$\frac{3}{a+2}-6\cdot \frac{a}{-4+a^2}=\frac{1}{a-2}$

$\frac{3}{a+2}-\frac{6a}{-4+a^2}=\frac{1}{a-2}$

$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}a+2,\:-4+a^2,\:a-2:\quad \left(a+2\right)\left(a-2\right)$

$\mathrm{Multiply\:by\:LCM=}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right)-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right)=\frac{1}{a-2}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right):\quad 3\left(a-2\right)$ $-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right):\quad -6a$ $\frac{1}{a-2}\left(a+2\right)\left(a-2\right):\quad a+2$

so equation becomes

$3\left(a-2\right)-6a=a+2$

-3a-6=a+2

-3a-6+6=a+2+6

-4a=8

$\mathrm{Divide\:both\:sides\:by\:}-4$

$\frac{-4a}{-4}=\frac{8}{-4}$

a=-2

$\mathrm{Verify\:Solutions}$

$\mathrm{Take\:the\:denominator\left(s\right)\:of\:}\frac{3}{a+2}-6\frac{a}{-4+a^2}-\frac{1}{a-2}\mathrm{\:and\:compare\:to\:zero}$

$\mathrm{Solve\:}\:a+2=0:\quad a=-2$

$\mathrm{Solve\:}\:-4+a^2=0:\quad a=2,\:a=-2$

$\mathrm{Solve\:}\:a-2=0:\quad a=2$

So the following points are undefined

$a=-2,\:a=2$

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

Answer from: Quest

Weiiejjrjfjjffjffkdkdod

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

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A student solves the following equation and determines that the solution is -2. Is the student correct? Explain. 3/a+2 - 6a/a^2-4 = 1/a-2

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Questions in other subjects:

A student solves the following equation and
determines that the solution is -2. Is the student
correct? Explain.
3/a+2 - 6a/a^2-4 = 1/a-2