anonymous
  • anonymous
Help with adding rational expressions. How do I add 5+ sqrt(x) + (1/1+x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[5+ \sqrt(x) + (1 \div (1+x))\]
Nnesha
  • Nnesha
\[\huge\rm 5+\sqrt{x} +\frac{1}{1+x}\] find the common denominator
Nnesha
  • Nnesha
5+sqrt{x} is same as 5+sqrt{x} over one \[\huge\rm \frac{5+\sqrt{x}}{1} +\frac{1}{1+x}\] so what is the common denominator

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anonymous
  • anonymous
1+x?
Nnesha
  • Nnesha
yes right so when we find common denominator we should multiply the numerator of 1st fraction by the denominator of 2nd fraction and multiply the numerator of 2nd fraction by the denominator of 1st fraction (just like cross multiply\[\huge\rm \frac{ (1+x)(5+\sqrt{x} )+1(1)}{ 1+x }\] )|dw:1442176038130:dw|
Nnesha
  • Nnesha
now use the foil method to multiply (1+x)(5 +Sqrt{5}) = ?
anonymous
  • anonymous
5 + sqrt(5) + 5x +5sqrt(5)
anonymous
  • anonymous
sorry xsqrt(5)
Nnesha
  • Nnesha
how did you get sqrt{5} ??
anonymous
  • anonymous
in your answer you wrote sqrt(5) 5 + sqrt(x) + 5x +xsqrt(x)
Nnesha
  • Nnesha
in the drawing ?
Nnesha
  • Nnesha
ohh wait nvm sorry about that
Nnesha
  • Nnesha
yes right now combine like terms \[\huge\rm \frac{ 5+\sqrt{x}+5x+x\sqrt{x}+1}{ 1+x }\] )
anonymous
  • anonymous
(6 +5x + xsqrt(x) + sqrt(x)) / (1+x)
Nnesha
  • Nnesha
yes right there is one more step you can convert square root to 1/2 \[\huge\rm \frac{ 5+\sqrt{x}+5x+ \color{red}{x\sqrt{x}}+1}{ 1+x }\] ) \[\huge\rm \frac{ 5+\sqrt{x}+5x+ \color{red}{x^1 \times x^{\frac{1}{2}}}+1}{ 1+x }\] ) apply the exponent rule when we multiply same bases we should add their exponents
Nnesha
  • Nnesha
\[\huge\rm x^m \times x^n=x^{m+n}\] so \[\huge\rm x^1 \times x^{\frac{1}{2}}=??\]
anonymous
  • anonymous
x^3/2
Nnesha
  • Nnesha
yes right that's it! nice job! :=)
anonymous
  • anonymous
thanks!
Nnesha
  • Nnesha
yw :=)

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