Thread: simplifying help

i havent taken an algebra class for sometime and im curious...how do i approach at simplifying the following denominator

3/(4x²+5x+1) so i can perform partial fraction integration

Originally Posted by maybnxtseasn

i havent taken an algebra class for sometime and im curious...how do i approach at simplifying the following denominator

3/(4x²+5x+1) so i can perform partial fraction integration

Dear maybnxtseasn,





Decomposing this into partial fractions;



Hope you can continue with the integration.

thanks but im curious as to the steps u use to simplify this?

Are you asking how he knew ? If so, one method is as follows:

The product of the coefficients of the first and last terms is .

and are factors of (the product from the previous step) and sum to (the coefficient of the middle term). So, write the middle term, , as : .

Then, group each pair of terms together: .

Perform any factoring on each group of terms: .

Now, factor : .

Another way to do that (but much more complicated that just factoring directly) is to solve the equation - not by factoring, of course, but by the quadratic formula:
[tex]x= \frac{-5\pm\sqrt{5^2- 4(4)(1)}}{2(4)}= \frac{-5\pm\sqrt{25- 16}}{8}= \frac{-5\pm\sqrt{9}}{8}= \frac{-5\pm3}{8}[tex]
so that and

Now, we can say that [tex]4x^2+ 5x+ 1= 4(x+ \frac{1}{4})(x- 1)= (4x+ 1)(x- 1)[/quote]
(I put the "4" in front to make t he leading coefficient 4.)

That is, as I said, the hard way!

Originally Posted by HallsofIvy

Another way to do that (but much more complicated that just factoring directly) is to solve the equation - not by factoring, of course, but by the quadratic formula:
[tex]x= \frac{-5\pm\sqrt{5^2- 4(4)(1)}}{2(4)}= \frac{-5\pm\sqrt{25- 16}}{8}= \frac{-5\pm\sqrt{9}}{8}= \frac{-5\pm3}{8}[tex]
so that and

Now, we can say that [tex]4x^2+ 5x+ 1= 4(x+ \frac{1}{4})(x- 1)= (4x+ 1)(x- 1)
(I put the "4" in front to make t he leading coefficient 4.)

That is, as I said, the hard way!

Dear HallsofIvy,

You new avatar make some of the text unreadable. I have seen this in your recent post a number of times and I tried the zoom in/out feature in the browser to eliminate the problem. But it was not helpful. Dont know if this is only a problem with my browser but anyhow I have included a screenshot so that you get an idea about how I see your post.