Responder
a) \( \frac{b}{a} \)
b) \( \frac{9}{x^{2}+6x+9} \)
c) \( 6x^{2} \)
d) \( \frac{x+3}{3x^{3}} \)
e) \( 1 \)
f) \( \frac{a^{2}-2a+1}{a^{2}} \)
Solución
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(ab-a^{2}\right)}{\left(b^{2}-a^{2}\right)}}{\left(\frac{a^{2}}{\left(b^{2}+ab\right)}\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{ab-a^{2}}{b^{2}-a^{2}}}{\frac{a^{2}}{b^{2}+ab}}\)
- step2: Divide the terms:
\(\frac{\frac{a}{b+a}}{\frac{a^{2}}{b^{2}+ab}}\)
- step3: Multiply by the reciprocal:
\(\frac{a}{b+a}\times \frac{b^{2}+ab}{a^{2}}\)
- step4: Reduce the fraction:
\(\frac{1}{b+a}\times \frac{b^{2}+ab}{a}\)
- step5: Rewrite the expression:
\(\frac{1}{b+a}\times \frac{b\left(b+a\right)}{a}\)
- step6: Reduce the fraction:
\(1\times \frac{b}{a}\)
- step7: Multiply the terms:
\(\frac{b}{a}\)
Calculate or simplify the expression \( (2*x^2-6*x)/(x^2-1) / ((x-3)/(x^2-x)) / (1/(3*x+3)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\frac{\left(2x^{2}-6x\right)}{\left(x^{2}-1\right)}}{\left(\frac{\left(x-3\right)}{\left(x^{2}-x\right)}\right)}}{\left(\frac{1}{\left(3x+3\right)}\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{\frac{2x^{2}-6x}{x^{2}-1}}{\frac{x-3}{x^{2}-x}}}{\frac{1}{3x+3}}\)
- step2: Divide the terms:
\(\frac{\frac{2x^{2}}{x+1}}{\frac{1}{3x+3}}\)
- step3: Multiply by the reciprocal:
\(\frac{2x^{2}}{x+1}\times \left(3x+3\right)\)
- step4: Rewrite the expression:
\(\frac{2x^{2}}{x+1}\times 3\left(x+1\right)\)
- step5: Reduce the fraction:
\(2x^{2}\times 3\)
- step6: Multiply the terms:
\(6x^{2}\)
Calculate or simplify the expression \( (3*x^2+27)/(2*x+6) * (6*x-18)/(x^4-81) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(3x^{2}+27\right)}{\left(2x+6\right)}\times \left(6x-18\right)}{\left(x^{4}-81\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{3x^{2}+27}{2x+6}\times \left(6x-18\right)}{x^{4}-81}\)
- step2: Multiply the terms:
\(\frac{\frac{\left(3x^{2}+27\right)\left(3x-9\right)}{x+3}}{x^{4}-81}\)
- step3: Multiply by the reciprocal:
\(\frac{\left(3x^{2}+27\right)\left(3x-9\right)}{x+3}\times \frac{1}{x^{4}-81}\)
- step4: Rewrite the expression:
\(\frac{3\left(x^{2}+9\right)\left(3x-9\right)}{x+3}\times \frac{1}{\left(x^{2}+9\right)\left(x^{2}-9\right)}\)
- step5: Reduce the fraction:
\(\frac{3\left(3x-9\right)}{x+3}\times \frac{1}{x^{2}-9}\)
- step6: Rewrite the expression:
\(\frac{3\times 3\left(x-3\right)}{x+3}\times \frac{1}{\left(x-3\right)\left(x+3\right)}\)
- step7: Reduce the fraction:
\(\frac{3\times 3}{x+3}\times \frac{1}{x+3}\)
- step8: Multiply the terms:
\(\frac{9}{\left(x+3\right)\left(x+3\right)}\)
- step9: Multiply the terms:
\(\frac{9}{\left(x+3\right)^{2}}\)
- step10: Calculate:
\(\frac{9}{x^{2}+6x+9}\)
Calculate or simplify the expression \( (a^2-2*a+1)/(a^2+2*a+1) * (a^2-1)/(a^2) * (a^2+a)/(a^2-a) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\frac{\left(a^{2}-2a+1\right)}{\left(a^{2}+2a+1\right)}\times \left(a^{2}-1\right)}{a^{2}}\times \left(a^{2}+a\right)}{\left(a^{2}-a\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{\frac{a^{2}-2a+1}{a^{2}+2a+1}\times \left(a^{2}-1\right)}{a^{2}}\times \left(a^{2}+a\right)}{a^{2}-a}\)
- step2: Multiply the terms:
\(\frac{\frac{\frac{\left(a^{2}-2a+1\right)\left(a-1\right)}{a+1}}{a^{2}}\times \left(a^{2}+a\right)}{a^{2}-a}\)
- step3: Divide the terms:
\(\frac{\frac{\left(a^{2}-2a+1\right)\left(a-1\right)}{a^{2}\left(a+1\right)}\times \left(a^{2}+a\right)}{a^{2}-a}\)
- step4: Multiply the terms:
\(\frac{\frac{\left(a^{2}-2a+1\right)\left(a-1\right)}{a}}{a^{2}-a}\)
- step5: Multiply by the reciprocal:
\(\frac{\left(a^{2}-2a+1\right)\left(a-1\right)}{a}\times \frac{1}{a^{2}-a}\)
- step6: Rewrite the expression:
\(\frac{\left(a-1\right)^{2}\left(a-1\right)}{a}\times \frac{1}{a\left(a-1\right)}\)
- step7: Reduce the fraction:
\(\frac{\left(a-1\right)\left(a-1\right)}{a}\times \frac{1}{a}\)
- step8: Multiply the terms:
\(\frac{\left(a-1\right)^{2}}{a\times a}\)
- step9: Multiply the terms:
\(\frac{\left(a-1\right)^{2}}{a^{2}}\)
- step10: Calculate:
\(\frac{a^{2}-2a+1}{a^{2}}\)
Calculate or simplify the expression \( (x^2+x-6)/(3*x^2-12*x) / ((x^3-2*x^2)/(x^2-16)) * (1/(x+4)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(x^{2}+x-6\right)}{\left(3x^{2}-12x\right)}}{\left(\frac{\left(x^{3}-2x^{2}\right)}{\left(x^{2}-16\right)}\right)}\times \left(\frac{1}{\left(x+4\right)}\right)\)
- step1: Remove the parentheses:
\(\frac{\frac{x^{2}+x-6}{3x^{2}-12x}}{\frac{x^{3}-2x^{2}}{x^{2}-16}}\times \left(\frac{1}{x+4}\right)\)
- step2: Remove the parentheses:
\(\frac{\frac{x^{2}+x-6}{3x^{2}-12x}}{\frac{x^{3}-2x^{2}}{x^{2}-16}}\times \frac{1}{x+4}\)
- step3: Divide the terms:
\(\frac{\left(x+3\right)\left(x+4\right)}{3x^{3}}\times \frac{1}{x+4}\)
- step4: Reduce the fraction:
\(\frac{x+3}{3x^{3}}\times 1\)
- step5: Multiply the terms:
\(\frac{x+3}{3x^{3}}\)
Calculate or simplify the expression \( (a^2*b-a*b)/(a^3+a^2) / ((a^2*b-2*a*b+b)/(a^3-a)) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(a^{2}b-ab\right)}{\left(a^{3}+a^{2}\right)}}{\left(\frac{\left(a^{2}b-2ab+b\right)}{\left(a^{3}-a\right)}\right)}\)
- step1: Remove the parentheses:
\(\frac{\frac{a^{2}b-ab}{a^{3}+a^{2}}}{\frac{a^{2}b-2ab+b}{a^{3}-a}}\)
- step2: Divide the terms:
\(\frac{\frac{ab-b}{a^{2}+a}}{\frac{a^{2}b-2ab+b}{a^{3}-a}}\)
- step3: Divide the terms:
\(\frac{\frac{ab-b}{a^{2}+a}}{\frac{ab-b}{a^{2}+a}}\)
- step4: Divide the terms:
\(1\)
Here are the simplified results for each part of the problem:
a)
\[
\frac{a b-a^{2}}{b^{2}-a^{2}} \div \frac{a^{2}}{b^{2}+a b} = \frac{b}{a}
\]
b)
\[
\frac{3 x^{2}+27}{2 x+6} \times \frac{6 x-18}{x^{4}-81} = \frac{9}{x^{2}+6x+9}
\]
c)
\[
\frac{2 x^{2}-6 x}{x^{2}-1} \div \frac{x-3}{x^{2}-x} \div \frac{1}{3 x+3} = 6x^{2}
\]
d)
\[
\frac{x^{2}+x-6}{3 x^{2}-12 x} \div \frac{x^{3}-2 x^{2}}{x^{2}-16} \times \frac{1}{x+4} = \frac{x+3}{3x^{3}}
\]
e)
\[
\frac{a^{2} b-a b}{a^{3}+a^{2}} \div \frac{a^{2} b-2 a b+b}{a^{3}-a} = 1
\]
f)
\[
\frac{a^{2}-2 a+1}{a^{2}+2 a+1} \times \frac{a^{2}-1}{a^{2}} \times \frac{a^{2}+a}{a^{2}-a} = \frac{a^{2}-2a+1}{a^{2}}
\]
If you need further explanations or steps for any of these simplifications, feel free to ask!
Respondido por UpStudy AI y revisado por un tutor profesional
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