Activity_2
1. in a furniture company the three employees. read their which stated that their basic olacy is Php15.000 plus a 10% commission for every famoure famare worth less than Php. 20.000.12% commission for 12% commission for every fumita worth Dbp 200,00 up to Php 45,000, and a compassion of 15% for every fucniture above 1. Php 45.000 Write a piece-wise function for this problem:
1. in a furniture company the three employees. read their which stated that their basic olacy is Php15.000 plus a 10% commission for every famoure famare worth less than Php. 20.000.12% commission for 12% commission for every fumita worth Dbp 200,00 up to Php 45,000, and a compassion of 15% for every fucniture above 1. Php 45.000 Write a piece-wise function for this problem:
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The expression simplifies as follows :
{\small{{\boxed{\rm{{\frac{x + y}{x - y} \: + \frac{x -y }{x + y} - \frac{2( {x}^{2 } - {y}^{3} )}{ {x}^{2} - {y}^{2} } }}}}}}
x−y
x+y
+
x+y
x−y
−
x
2
−y
2
2(x
2
−y
3
)
{\small{{\boxed{\rm{{ = \frac { (x \: +y)(x \: + y) + (x - y)(x - y) - 2( {x}^{2} - {y}^{2}) } {(x - y)(x + y)} }}}}}}
=
(x−y)(x+y)
(x+y)(x+y)+(x−y)(x−y)−2(x
2
−y
2
)
{\small{{\boxed{\rm{{ = \frac{(x + {y)}^{2} + (x - y) - 2( {x}^{2 } - {y}^{3}) }{ {x}^{2} - {y}^{2} } }}}}}}
=
x
2
−y
2
(x+y)
2
+(x−y)−2(x
2
−y
3
)
{\small{{\boxed{\rm{{ \frac{( {x}^{2} + 2xy + {y}^{2} ) + ( {x}^{2 } - 2xy + {y}^{2}) - 2( {x}^{2} - {y}^{2}) }{ {x}^{2} - {y}^{2} } }}}}}}
x
2
−y
2
(x
2
+2xy+y
2
)+(x
2
−2xy+y
2
)−2(x
2
−y
2
)
{\small{{\boxed{\rm{{ = \frac{2( {x}^{2} + {y} ^{2} - ( {x}^{2} - {y}^{2}) }{ {x}^{2} - {y}^{2} } }}}}}} = {\small{\underline{\boxed{\rm{\pink{ \frac{4 {y}^{2} }{ {x}^{2} - {y}^{2} } }}}}}}
=
x
2
−y
2
2(x
2
+y
2
−(x
2
−y
2
)
=
x
2
−y
2
4y
2
In order to simplify the addition of the algebraic fraction the first step is to figure out the LCM of the denominator and that is (x-y)(x+y) now divide the LCM by the denominator of very fraction and multiply the result by the numerator which yields
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Step-by-step explanation:
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