How can I simplify this fraction: (x+2)/(x-1) * (4x+1)/(x-1)?

  • Context: High School 
  • Thread starter Thread starter DLxX
  • Start date Start date
  • Tags Tags
    Simplify
Click For Summary
SUMMARY

The discussion focuses on simplifying the fraction (x+2)/(x-1) * (4x+1)/(x-1). Participants confirm that the correct method involves inverting the denominator and multiplying, which leads to the expression (x+2)/(x-1) * (x-1)/(4x+1). The x-1 terms cancel out, simplifying the fraction to (x+2)/(4x+1). This method is a standard approach to dividing fractions, reinforcing foundational algebra concepts.

PREREQUISITES
  • Understanding of basic algebraic operations
  • Familiarity with fraction manipulation
  • Knowledge of the reciprocal of a fraction
  • Experience with simplifying algebraic expressions
NEXT STEPS
  • Study the properties of fractions and their simplification techniques
  • Learn about algebraic identities and their applications
  • Explore advanced fraction operations, including complex fractions
  • Practice problems involving rational expressions and their simplification
USEFUL FOR

Students learning algebra, educators teaching fraction simplification, and anyone seeking to improve their mathematical problem-solving skills.

DLxX
Messages
58
Reaction score
0
[tex]\frac {x+2} {x-1} \frac \frac {4x+1} {x-1}[/tex]

Would using the bowtie method work? Cross multiply and then subtract the two answers found from each other, and put that result over the multiplaction of the two denominators. ?

EDIT: I messed up the Latex thing. THe 4x-1 and the x-1 are supposed to be a fraction under the x+2/x-1
 
Mathematics news on Phys.org
So you mean

[tex]\frac{\frac{x+2}{x-1}}\frac{4x+1}{x-1}}[/tex]
?

You learned how to divide fractions in the fourth grade: invert the denominator and multiply. This is:
[tex]\frac{x+2}{x-1}*\frac{x-1}{4x+1}[/tex]

Can you reduce that?
 
Agreed. Dividing is the same as multiplying by the reciprocal. So when you do this the [tex]x - 1[/tex]'s cancel out.
 

Similar threads

MHB Solutions of an inequality (1-√(1-4x^2)/x < 3
  • · Replies 4 ·
Replies
4
Views
2K
MHB Inequality with fractions solve 2/(x^2−1)≤1/(x+1)
  • · Replies 9 ·
Replies
9
Views
2K
MHB Partial fraction problem (x^2)/[(x-2)(x+3)(x-1)]
  • · Replies 4 ·
Replies
4
Views
3K
High School Adding 'x' to 'xy' for Resultant <=1: A Table Guide
  • · Replies 18 ·
Replies
18
Views
3K
MHB Evaluate Fraction: Simplify $\frac {x^2 + 1 - 1}{x^2 + 1}$
  • · Replies 2 ·
Replies
2
Views
2K
High School Could someone verify how this simplifies?
  • · Replies 15 ·
Replies
15
Views
2K
MHB Fraction Question: How to Solve 1/6(3/4x-2)=-1/5?
  • · Replies 10 ·
Replies
10
Views
2K
High School Fractional/decimal powers
  • · Replies 10 ·
Replies
10
Views
3K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
  • · Replies 10 ·
Replies
10
Views
2K
MHB Finding Domain of f(x)=\frac{1}{x^{2}-x-6}
  • · Replies 5 ·
Replies
5
Views
3K