How do you multiply # x / 10 - 1/2 =-3 /(5x)#?

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Answer 1 · 2015-05-09T08:38:58

Given:
# x/10 - 1/2 = -3/(5x)#

to make the denominator of the L.H.S equal we take the L.C.M:

L.C.M of 10 and 2 #=# 10

# (x/10) - (1 xx 5)/(2 xx5) = -3/(5x)#
# (x/10) - (5)/10 = -3/(5x)#

# (x- 5)/10 = -3/(5x)#
on cross multiplying:

# (x- 5) xx (5x) = -3 xx 10#

# 5x^2 - 25x = -30#

# 5x^2 - 25x + 30 = 0#

dividing the equation by 5:
# x^2 - 5x + 6 = 0#

solving this equation by grouping / splitting the middle term:

# x^2 - 2x -3x + 6 = 0# (#2 xx 3 = 6 and 2+ 3 = 5#)

# = x (x - 2) - 3(x - 2)#

# = (x - 2) (x - 3)#

#x # has two values here:
#x = 2 and x=3#