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

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In summary, the conversation discusses dividing fractions using the bowtie method and the fourth grade method of inverting the denominator and multiplying. The suggestion to cross multiply and subtract the answers is also mentioned, along with the possibility of reducing the resulting fraction.
  • #1
DLxX
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[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
 
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  • #2
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?
 
  • #3
Agreed. Dividing is the same as multiplying by the reciprocal. So when you do this the [tex] x - 1[/tex]'s cancel out.
 

1. How do I simplify an equation?

To simplify an equation, you need to combine like terms, eliminate any parentheses, and use the correct order of operations. Begin by combining any like terms by adding or subtracting their coefficients. Then, use the distributive property to eliminate parentheses. Finally, use the correct order of operations (PEMDAS) to simplify any remaining terms.

2. Can I simplify fractions?

Yes, fractions can be simplified by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it. This will reduce the fraction to its simplest form. Keep in mind that you should also simplify any mixed numbers by converting them to improper fractions first.

3. How do I simplify radicals?

To simplify radicals, you need to find the perfect square factor of the number inside the radical. Then, you can take the square root of that perfect square and move it outside of the radical. The remaining number inside the radical should be simplified as much as possible. If the radical has a coefficient, you can also simplify it by finding the factors of that coefficient.

4. What is the difference between simplifying and solving?

Simplifying involves reducing an equation or expression to its simplest form. This means combining like terms, eliminating parentheses, and using the correct order of operations. Solving, on the other hand, involves finding the value of a variable in an equation or expression. This requires additional steps such as isolating the variable and using inverse operations to solve for it.

5. How do I know when an expression is fully simplified?

An expression is fully simplified when there are no like terms left to combine, no parentheses remaining to eliminate, and no more operations that can be performed. Additionally, if the expression contains fractions, they should be reduced to their simplest form and any radicals should be simplified as much as possible.

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