Question

Stiind ca x/5=y/6, determinati:
a) (2x+3y)/(4x+5y)
b) (7x^2-2y^2)/(2x^2+3y^2)

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{x}{5} =\frac{y}{6} =>y=\frac{6x}{5}$

$2x+3y=2x+3*\frac{6x}{5} =\frac{2x*5+18x}{5}=\frac{28x}{5}$

$4x+5y=4x+5*\frac{6x}{5} =4x+6x=10x$

$=>\frac{2x+3y}{4x+5y}=\frac{\frac{28x}{5} }{10x} =\frac{28x}{10x*5}=\frac{14}{25}$

$7x^{2} -2y^{2} =7x^{2}-2*(\frac{6x}{5} )^{2} =7x^{2} -2*\frac{36x^{2} }{25}=\frac{175x^{2} -72x^{2} }{25}=\frac{103x^{2} }{25}$

$2x^{2} +3y^{2}=2x^{2} +3*(\frac{6x}{5})^{2} =2x^{2} +3*\frac{36x^{2} }{25}=\frac{50x^{2} +108x^{2} }{25}=\frac{158x^{2} }{25}$

$=> \frac{7x^{2}-2y^{2} }{2x^{2} +3y^{2} }=\frac{\frac{103x^{2} }{25} }{\frac{158x^{2} }{25} }= \frac{103}{158}$

$conditii-de-existenta:x\neq 0$