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anonymous

  • one year ago

Help with adding rational expressions. How do I add 5+ sqrt(x) + (1/1+x)

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  1. anonymous
    • one year ago
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    \[5+ \sqrt(x) + (1 \div (1+x))\]

  2. Nnesha
    • one year ago
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    \[\huge\rm 5+\sqrt{x} +\frac{1}{1+x}\] find the common denominator

  3. Nnesha
    • one year ago
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    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

  4. anonymous
    • one year ago
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    1+x?

  5. Nnesha
    • one year ago
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    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|

  6. Nnesha
    • one year ago
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    now use the foil method to multiply (1+x)(5 +Sqrt{5}) = ?

  7. anonymous
    • one year ago
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    5 + sqrt(5) + 5x +5sqrt(5)

  8. anonymous
    • one year ago
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    sorry xsqrt(5)

  9. Nnesha
    • one year ago
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    how did you get sqrt{5} ??

  10. anonymous
    • one year ago
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    in your answer you wrote sqrt(5) 5 + sqrt(x) + 5x +xsqrt(x)

  11. Nnesha
    • one year ago
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    in the drawing ?

  12. Nnesha
    • one year ago
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    ohh wait nvm sorry about that

  13. Nnesha
    • one year ago
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    yes right now combine like terms \[\huge\rm \frac{ 5+\sqrt{x}+5x+x\sqrt{x}+1}{ 1+x }\] )

  14. anonymous
    • one year ago
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    (6 +5x + xsqrt(x) + sqrt(x)) / (1+x)

  15. Nnesha
    • one year ago
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    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

  16. Nnesha
    • one year ago
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    \[\huge\rm x^m \times x^n=x^{m+n}\] so \[\huge\rm x^1 \times x^{\frac{1}{2}}=??\]

  17. anonymous
    • one year ago
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    x^3/2

  18. Nnesha
    • one year ago
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    yes right that's it! nice job! :=)

  19. anonymous
    • one year ago
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    thanks!

  20. Nnesha
    • one year ago
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    yw :=)

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