Question

Which of the following algebraic expressions are rational: a.) x^2-3x+4x=8/4, b.) 1/(3x) + 4x/6 =1, c.) 5/x +x/9=2/4, d.) x^2 -3x+4x=0, e.) 3+ (4x/6)=1

Answer 1

 A rational expression is a fraction in which the denominator and/or the numerator are polynomials.

Let us analyse each expressions with respect to the definition given above.

a). x²-3x+4x =8/4

This can be written as $\frac{x²-3x+4x}{1}$ = $\frac{8}{4}$

Since the equation can be written in this form, that implies, it is rational.

b). 1/(3x) + 4x/6 =1

Let us make the L.H.S. a single fraction

$\frac{1}{3x} + \frac{4x}{6} = 1$

Find the L.C.M.

$\frac{2+4x²}{6x} = 1$

Since the equation 1/(3x) + 4x/6 =1 can be written as $\frac{2+4x²}{6x} = \frac{1}{1}$

That implies it is rational.

c).5/x +x/9=2/4

Let us make the L.H.S. a single fraction.

$\frac{5}{x} + \frac{x}{9} = \frac{2}{4}$

Find the L.C.M.

$\frac{45+x²}{9x} = \frac{2}{4}$

Since the equation 5/x +x/9=2/4 can be written as $\frac{45+x²}{9x} = \frac{2}{4}$

That implies it is rational

d).x² -3x+4x=0

This can be written as $\frac{x²-3x+4x}{1}=\frac{0}{1}$

Since the equation can be written in this form, that implies it is rational.

e).3+ (4x/6)=1

Let us make the L.H.S. a single fraction

$\frac{3}{1} + \frac{4x}{6} = \frac{1}{1}$

Find the L.C.M.

$\frac{18+4x}{6} = \frac{1}{1}$

Since the equation 3+ (4x/6)=1 can be written as $\frac{18+4x}{6} = \frac{1}{1}$

That implies it is rational.