Rational Function

[JSmith]

Solve 7/3 = (5/x) + 4.
7x=15 + 4 (cross multiply)
7x=19

is that correct?

 

[Deleted member 4993]

Solve 7/3 = (5/x) + 4.
7x=15 + 4 (cross multiply) ........... You cannot cross-multiply like that. Better method is - multiply both sides by 3*x (LCD):

7 *x = 15 + 12*x

x = -3

Check

5/x + 3 = 5/(-3) + 4 = (5 - 12)/(-3) = (-7)/(-3) = 7/3

Checks....


7x=19

is that correct?

.

 

[HallsofIvy]

Solve 7/3 = (5/x) + 4.
7x=15 + 4 (cross multiply)

No, you have to multiply (3x)(5/x+ 4)= 15+ 12x, not 15+ 4.

7x=19

is that correct?

 

[mmm4444bot]

Cross-multiplication works when you have two ratios (fractions) set equal to one another.

You were not given two equal ratios:

\(\displaystyle \dfrac{7}{3} = \dfrac{5}{x} + 4\)



If you desire to apply cross-multiplication above, then you must first combine 5/x+4 into a single ratio.

\(\displaystyle \dfrac{7}{3} = \dfrac{5 + 4x}{x}\)



But clearing fractions in the original equation, as previously described, is less steps. :cool:

 

[Deleted member 4993]

This is the reason for eliminating "cross-multiplication" from the middle/high school vocabulary.