Good day everyone.
I have three questions relating to simplifying algebraic questions, and what intimidates me the most are the denominators. Here are the questions:
1.
2.
3.
Here are my workings respectively:
1.
?
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2.
?
I am so sorry that I couldn't do it further. I felt mortified when my answers are wrong. Please find my faults and explain how I should have done. Thank you.
PythagorasNeophyte
The first and third problems you can simplify with partial fractions. Have you learned partial fractions?
The second problem, just multiply the numerator and denominator by x + 3 of the first fraction.
Now you can complete combining the fractions with my instructions.
I'm not sure why you suggested partial fractions. In partial fractions you are usually given a single fraction and you want to decompose it into a sum/difference of fractions. What the OP wants to do is the other way around -- combine multiple fractions into a single fraction.
The other expressions you suggest are common denominators; they are just not the LEAST common denominator.
Look at what we do with finding the LCM of two numbers Consider 2 and 10.
The prime factors of 2 is just 2.
The prime factors of 10 is 2 x 5.
2 goes into 10. If one number goes into another then the LCM is just the larger number, or in our case, 10.
If we were to apply what you suggested to this case, you would be claiming that the LCM is or 20. You want to "grab" the 2 factor from both numbers. But we don't need to do that.
It's the same with expressions.
The factors of x - 3 is just (x - 3).
The factors of is (x - 3)(x + 3).
x - 3 "goes into" [maht]x^2 - 9[/tex], so the LCM is the "larger" expression, or [maht]x^2 - 9[/tex].