Rational Expressions Problem....just one...10 points!?

Think about how you would simplify the following:

3/5 - 4/12

The same principles carry over to algebra.

Start by reducing fractions are in lowest terms by finding common factors.

Then find the lowest common denominator between the two fractions. Rewrite each to have that denominator. Now you can perform the subtraction.

Combine like terms if there are any. finally, make sure your answer is in lowest terms.

Look at the denominator of the second term, the 4x + 12. You can pull out the common term of 4 to simplify it to be 4(x+3).

Now, you can cancel out one of the (x+3) terms from the numerator of the first term, along with cancelling out the (x+3) from the denominator of the second term.

After doing those two things, your second term looks like this: (4y^2)/4x. You can cancel out a 4 from the top and bottom, leaving you with (y^2)/x.

The whole equation now looks like this: (x+3)/x^2 times (y^2)/x. Now, multiply these two terms together to get:

(x+3)(y^2)/x^3

That expression is fully simplified, and you're done! Hope this helps.

in the 1st equation, the two the numerator and the denominator could be factored employing the guideline of the adaptation between 2 suited squares. so which you finally end up with (x^2 + 4)(x^2 - 4) / (x^2 + a million) (x^2 -a million). once you get that, you spot which you will cancel out the (x^2 + 4) and the (x^2 + a million) bc they're the two in the 2d equation. you finally end up with (x^2 - 4) / (x^2 -a million). Now you're able to desire to simplify, and you will try this by using factoring the adaptation of two suited squares back. the respond is (x+2) (x - 2) / (x+a million) (x - a million). wish that's obvious.

= (x + 3)^2 / x^2 * y^2 / (x + 3)

= (x + 3) y^2/x^2