Simplifying a fraction of polynomials












0












$begingroup$


This is a really simple question. All I want to know is how it goes from that first line of the equation to the second line, what is it they're doing. I'm just missing something, can someone explain.
$$
begin{split}
H(z) &= frac{0.3249(z+1)}{(z-1)+0.3249z+0.3249}\
H(z) &= frac{0.3249(z+1)}{1.3249z-0.6751}
end{split}
$$






algebra-precalculus polynomials







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  • $begingroup$
    $begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
    $endgroup$
    – Bill Dubuque
    Jan 8 at 17:34


















0












$begingroup$


This is a really simple question. All I want to know is how it goes from that first line of the equation to the second line, what is it they're doing. I'm just missing something, can someone explain.
$$
begin{split}
H(z) &= frac{0.3249(z+1)}{(z-1)+0.3249z+0.3249}\
H(z) &= frac{0.3249(z+1)}{1.3249z-0.6751}
end{split}
$$






algebra-precalculus polynomials







share|cite|improve this question











$endgroup$












  • $begingroup$
    $begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
    $endgroup$
    – Bill Dubuque
    Jan 8 at 17:34
















0












0








0





$begingroup$


This is a really simple question. All I want to know is how it goes from that first line of the equation to the second line, what is it they're doing. I'm just missing something, can someone explain.
$$
begin{split}
H(z) &= frac{0.3249(z+1)}{(z-1)+0.3249z+0.3249}\
H(z) &= frac{0.3249(z+1)}{1.3249z-0.6751}
end{split}
$$






algebra-precalculus polynomials







share|cite|improve this question











$endgroup$




This is a really simple question. All I want to know is how it goes from that first line of the equation to the second line, what is it they're doing. I'm just missing something, can someone explain.
$$
begin{split}
H(z) &= frac{0.3249(z+1)}{(z-1)+0.3249z+0.3249}\
H(z) &= frac{0.3249(z+1)}{1.3249z-0.6751}
end{split}
$$






algebra-precalculus polynomials




algebra-precalculus polynomials






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edited Jan 8 at 17:16









gt6989b

33.9k22455




33.9k22455










asked Jan 8 at 17:13









controlled_controlled_

111




111












  • $begingroup$
    $begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
    $endgroup$
    – Bill Dubuque
    Jan 8 at 17:34




















  • $begingroup$
    $begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
    $endgroup$
    – Bill Dubuque
    Jan 8 at 17:34


















$begingroup$
$begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
$endgroup$
– Bill Dubuque
Jan 8 at 17:34






$begingroup$
$begin{align}{rm The denominator } &= color{#c00}z!-!1 + color{#c00}{az}!+!a\[.2em] &= color{#c00}{(a!+!1)z} +a!-!1 {rm for} a = 0.3249end{align}$
$endgroup$
– Bill Dubuque
Jan 8 at 17:34












1 Answer
1






active

oldest

votes


















2












$begingroup$

Note that the denominator can be simplified:
$$
(z-1) + 0.3249z + 0.3249 = (z + 0.3249z) + (0.3249-1) = 1.3249z - 0.6751.
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks very much
    $endgroup$
    – controlled_
    Jan 8 at 17:16











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1 Answer
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active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

Note that the denominator can be simplified:
$$
(z-1) + 0.3249z + 0.3249 = (z + 0.3249z) + (0.3249-1) = 1.3249z - 0.6751.
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks very much
    $endgroup$
    – controlled_
    Jan 8 at 17:16
















2












$begingroup$

Note that the denominator can be simplified:
$$
(z-1) + 0.3249z + 0.3249 = (z + 0.3249z) + (0.3249-1) = 1.3249z - 0.6751.
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks very much
    $endgroup$
    – controlled_
    Jan 8 at 17:16














2












2








2





$begingroup$

Note that the denominator can be simplified:
$$
(z-1) + 0.3249z + 0.3249 = (z + 0.3249z) + (0.3249-1) = 1.3249z - 0.6751.
$$






share|cite|improve this answer









$endgroup$



Note that the denominator can be simplified:
$$
(z-1) + 0.3249z + 0.3249 = (z + 0.3249z) + (0.3249-1) = 1.3249z - 0.6751.
$$







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 8 at 17:14









gt6989bgt6989b

33.9k22455




33.9k22455












  • $begingroup$
    thanks very much
    $endgroup$
    – controlled_
    Jan 8 at 17:16


















  • $begingroup$
    thanks very much
    $endgroup$
    – controlled_
    Jan 8 at 17:16
















$begingroup$
thanks very much
$endgroup$
– controlled_
Jan 8 at 17:16




$begingroup$
thanks very much
$endgroup$
– controlled_
Jan 8 at 17:16


















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