$\dfrac{3y}{y^2+7y+10}+\dfrac{2}{y+2}\\\\=\dfrac{3y}{(y+2)(y+5)}+\dfrac{2(y+5)}{(y+2)(y+5)}=\dfrac{3y+2(y+5)}{(y+2)(y+5)}\\\\=\dfrac{5y+10}{(y+2)(y+5)}=\dfrac{5(y+2)}{(y+2)(y+5)}=\boxed{\dfrac{5}{y+5}}$

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<em>Comment on rational expressions</em>

When writing ratios in plain text, it is imperative to put parentheses around numerators and denominators. (If the numerator is a product only, then parentheses are optional.)

Your expression might be properly written as ...

3y/(y^2 +7y +10) +2/(y+2)

As you have written it, it simplifies to ...

3(y/y)2 +7y +10 +2/y +2 = 3·2 +7y +2/y +12

= 7y +2/y +18

Please note, too, the exponentiation symbol (^).

6 0

3 years ago

Compute F(s), the Laplace transform of f(t) = e^(5t) (t^2 +4t +7)

MakcuM [25]

Recall that

$\mathcal L_s\{t^ne^{ct}\}=\dfrac{n!}{(s-c)^{n+1}}$

Then

$F(s)=\dfrac2{(s-5)^3}+\dfrac4{(s-5)^2}+\dfrac7{s-5}$

3 0

3 years ago