Rational exponents; what do i do???

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Jeyaganesh asked Jun 3, 2023

354,131 views

21 votes

Rational exponents; what do i do???

Mathematics
high-school

Jeyaganesh asked Jun 3, 2023

by Jeyaganesh

3.3k points

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1 Answer

15 votes

Answer:

$x = -\frac{48}5$

Step by step explanation:

$~~~~~~~(x^2+12x+36)/(2x^2)-(x^2 +7x +12)/(2x^2)= \frac 5{4x}\\\\\\\implies (x^2 +12x +36 -x^2 -7x -12)/(2x^2 ) = \frac 5{4x}\\\\\\\implies (5x+24)/(2x^2) = \frac 5{4x}\\\\\\\implies 4x(5x+24) = 5(2x^2)\\\\\\\implies 20x^2+96x= 10x^2\\\\\\\implies 20x^2 -10x^2 +96x=0\\\\\\\implies 10x^2 +96x= 0\\\\\\\implies 5x^2 +48x = 0\\\\\\\implies x(5x+48)=0\\\\\\\implies x = -\frac{48}5~~~~~;[x\\eq 0]$