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hichkok12 [17]
2 years ago
12

Simplify each sum or difference. State any restrictions on the variables.

Mathematics
1 answer:
Dvinal [7]2 years ago
7 0

Answer:

2(d-2)/(2d+1) or 1 - 5/(2d+1)

d can not be -½

Step-by-step explanation:

(d-3)/(2d+1) + (d-1)/(2d+1)

Lcm: 2d+1

(d-3+d-1)/(2d+1)

= (2d-4)/(2d+1)

= 2(d-2)/(2d+1)

If further simplification required:

= (2d-4)/(2d+1)

= (2d+1-5)/(2d+1)

= (2d+1)/(2d+1) - 5/(2d+1)

= 1 - 5/(2d+1)

2d+1 = 0

When d = -½

So d can not be -½ because when the denominator becomes 0, fraction becomes undefined

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\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&8730&j-w&9\\ \textit{with the wind}&7260&j+w&6 \end{array}~\hfill \begin{cases} 8730=(j-w)(9)\\ 7260=(j+w)(6) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{\cfrac{8730}{9}=j-w\implies }970=j-w\implies 970+w=j \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{using the 2nd equation}}{\cfrac{7260}{6}=j+w}\implies 1210=j+w\implies \stackrel{\textit{doing some substitution on \underline{j}}}{1210=(970+w)+w} \\\\\\ 1210=970+2w\implies 240=2w\implies \cfrac{240}{2}=w\implies \boxed{120=w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{970+w=j}\implies 970+120=j\implies \boxed{1090=j}

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