Please help?

Question

im having major trouble in algebra 2. do you think you can help me with this problem?

m^4x+m^5
------------- divided by m^3x^2-mx^4
m^3x-mx^3 -----------------
m^3x^3-x^6

thank you for helping!

Answer 1

PROBLEM 1:

m^4x + m^5
-----------------
m^3x² - mx^4

In the numerator you can factor out m^4:
m^4(x + m)

In the denominator, you can factor out mx²
mx²(m² - x²)

m^4(x + m)
---------------
mx²(m² - x²)

Now cancel one m from top and bottom:
m^3(x + m)
---------------
x²(m² - x²)

Here you have a difference of squares in the denominator. Remember the rule for factoring a difference of squares?
m² - x² = (m + x)(m - x)

m^3(x + m)
---------------
x²(m + x)(m - x)

Now cancel out the (x + m) and (m + x) from top and bottom:
m^3
------------
x²(m - x)

That's about as far as you can go...

PROBLEM 2:
m^3x - mx^3
-------------------
m^3x^3 - x^6

From the numerator, factor mx
mx(m² - x²)

From the denominator, factor x^3
x^3(m^3 - x^3)

mx(m² - x²)
--------------------
x^3(m^3 - x^3)

Cancel the x from top and bottom:
m(m² - x²)
--------------------
x²(m^3 - x^3)

Now you have a difference of squares in the numerator:
m(m + x)(m - x)
---------------------
x²(m^3 - x^3)

And a difference of cubes in the denominator. Here you have to remember the rule:
A^3 - B^3 = (A - B)(A² + AB + B²)

m(m + x)(m - x)
---------------------------
x²(m - x)(m² - mx - x²)

Cancel the (m - x) from top and bottom:
m(m + x)
---------------------
x²(m² - mx - x²)

Again, that is about as far as you can go.