Find the missing side length

What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?

Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

Given the equation:

$\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}$

Follow these steps to solve it:

- Subtract the fractions on the left side of the equation:

$\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}$

- Using the Difference of squares formula ( $a^2-b^2=(a+b)(a-b)$ ) we can simplify the denominator of the right side of the equation:

$\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}$

- Multiply both sides of the equation by $(m+3)(3-m)$ and simplify:

$\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}$

- Multiply both sides by $m-3$ :

$(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)$

- Apply Distributive property and simplify:

$(-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0$

- Divide both sides of the equation by -6:

$\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0$

- Factor the equation and solve for "m":

$(m-3)^2=0\\\\m=3$

In order to verify it, you must substitute $m=3$ into the equation and solve it:

$\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}$

<em>NO SOLUTION</em>

7 0

3 years ago

5x-(x+1)=5-2x i dont understand what to do. Plz help

Vlada [557]

Answer:

x=1

Step-by-step explanation:

5x-(x+1)=5-2x

distribute

5x-x-1 = 5-2x

4x-1 = 5-2x

add 2x on each side

4x-1+2x = 5-2x+2x

6x -1 = 5

add 1 on each side

6x-1+2 = 5+1

6x = 6

divide by 6

6x/6 = 6/6

x = 1

6 0

3 years ago

Evaluate the function at the given value and simplify.

Licemer1 [7]

Answer:

The correct option is b.

Step-by-step explanation:

The given function is

$f(x)=-5x+1$

We need to find the value of f(-2). It means we have to find the value of given function at x=-2.

Substitute x=-2 in the given function to find the value of f(-2).

$f(-2)=-5(-2)+1$

On simplification we get

$f(-2)=10+1$

$f(-2)=11$

The value of f(-2) is 11. Therefore the correct option is b.

8 0

3 years ago

Last month Maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. Let x re

r-ruslan [8.4K]

<span>The equation that can be used is 90-10y=5x. In order to get this answer, you first start with figuring out how many miles total were hiked for each trail. The 5-mile mountain trail total would be equal to 5x and the 10-mile canal trail total would be 10y. Adding both of these totals together would give you 90 miles and an equation of 5x+10y=90. All you do now is rearrange the equation by subtracting 10y from each side and you get 90-10y=5x.</span>

8 0

4 years ago

Read 2 more answers

Pls help 20 points!

Rasek [7]

Terms : 12x, 3, 13, 4x
Like Terms : 12x and 4x, 3 and 13
Coefficients: 12, 4
Constants : 3, 13

6 0

3 years ago

Read 2 more answers