Answer:
[tex]2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5} = \frac{47x-36}{12}[/tex]
Step-by-step explanation:
Considering the expression
[tex]2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5}[/tex]
Simplifying the expression
[tex]\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{4}=\frac{9}{4}[/tex]
[tex]\frac{9}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{5}=\frac{13}{5}[/tex]
[tex]\frac{9}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{3}=\frac{13}{3}[/tex]
[tex]\frac{9}{4}x+\left(\frac{13}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 7\frac{4}{5}=\frac{39}{5}[/tex]
[tex]\frac{9}{4}x+\left(\frac{13}{3}x-\frac{39}{5}\right)\div \frac{13}{5}[/tex]
As
[tex]\frac{9}{4}x=\frac{9x}{4}[/tex]
and
[tex]\frac{\frac{13}{3}x-\frac{39}{5}}{\frac{13}{5}}=\frac{5\cdot \frac{65x-117}{15}}{13}[/tex]
So,
[tex]\frac{9x}{4}+\frac{5\cdot \frac{65x-117}{15}}{13}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}4,\:13:\quad 52[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]
[tex]\frac{117x}{52}+\frac{\frac{4\left(65x-117\right)}{3}}{52}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]\mathrm{Join}\:117x+\frac{4\left(65x-117\right)}{3}:\quad \frac{611x-468}{3}[/tex]
[tex]\frac{\frac{611x-468}{3}}{52}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}[/tex]
[tex]\frac{611x-468}{3\cdot \:52}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:3\cdot \:52=156[/tex]
[tex]\frac{611x-468}{156}[/tex]
[tex]\mathrm{Factor}\:611x-468:\quad 13\left(47x-36\right)[/tex]
[tex]\frac{13\left(47x-36\right)}{156}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:13[/tex]
[tex]\frac{47x-36}{12}[/tex]
Therefore, [tex]2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5} = \frac{47x-36}{12}[/tex]
Keywords: algebraic expression
, simplification
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