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marishachu [46]
3 years ago
6

Show work and simplify the equation

Mathematics
1 answer:
disa [49]3 years ago
5 0
Hello,

if \ a \neq -3, a \neq 1, a \neq -5\\

 \dfrac{2a^2+5a-3}{a^2+8a+15}  *  \dfrac{a^2+4a-5}{3a^2-a-2} \\


= \dfrac{(a+3)(2a-1)}{(a+5)(a+3)} *  \dfrac{(a+5)(a-1)}{(a-1)(3a+2)} \\

= \dfrac{2a-1}{3a+2}

explains:

1)
a^2+4a-5=a^2+5a-a-5\\
=a(a+5)-(a+5)\\
=(a+5)(a-1)




2)
a^2+8a+15=a^2+5a+3a+15\\
=a(a+5)+3(a+5)\\
=(a+5)(a+3)


3)
a^2+4a-5=a^2+5a-a-5\\
=a(a+5)-(a+5)\\
=(a+5)(a-1)


4)
3a^2-a-2=3a^2-3a+2a-2\\
=3a(a-1)+2(a-1)\\
=(a-1)(3a+2)



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