Does the point ( 3 , 3 ) lie on the circle that is centered at the origin and contains the point (3, 0)? why?

If the center is at point (0,0) which is the origin and point (3,0) is along the circle, then that means the radius is 3 units. Now, let's find if point (3,3) is equal to the radius by using the distance formula. Let point 1 be (0,0) and point 2 be (3,3).

d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(3 - 0)² + (3 - 0)²]
d = 4.24 units

Since the distance is more than the length of radius, it means that point (3,3) lies outside the circle. 

Step-by-step explanation:

We have been given an equation . We are asked to find the solutions of our given equation.

First of all, we will cross multiply our given equation as:

Subtract from both sides:

Now we will factor out .

Now we will factor by splitting the middle term.

Now we will use zero product property and solve for x as:

Now, we will check for extraneous solutions.

We can see that will make both denominators zero because our function is not defined at  .

Therefore, the solution for our given equation is .