Ineed this is due at 11: 59 tonight!

Step-by-step explanation:

In order to rationalize the denominator, you must multiply the top and bottom by the bottom's conjugate. The conjugate of is . The reason we do this is because when you multiply conjugates, all you have to do is multiply first terms and last terms (of the foil method).

So we are doing:

You will have to use the full foil method on top:

Reorder top using commutative property to put "like terms" together:

Simplify:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions