How do you solve $\frac{a + 4}{2} = \frac{a + 4}{a}$ $(a+4)/2 = (a+4)/a$ ?

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Answer 1 · 2016-06-07T19:21:21

2, -4.

By first cross-multiplying 7 then trasposing, the eqn. becomes,
a(a+4)-2(a+4)=0, i.e., (a+4)(a-2)=0.

Hence the soln. : a=-4, a=2.

Answer 2 · 2016-06-07T19:21:52

$a = 2$ $a=2$

As the top values (numerators) are of the same value we could disregard them and simply write $a = 2$ $a=2$

However, I suspect the that question poser is looking for you to use algebraic manipulation. So hear goes!

Invert both sides giving:

$\frac{2}{a + 4} = \frac{a}{a + 4}$ $2/(a+4)=a/(a+4)$

Multiply both sides by $(a + 4)$ $(a+4)$ giving:

$2 \times \frac{a + 4}{a + 4} = a \times \frac{a + 4}{a + 4}$ $2xx(a+4)/(a+4)=axx(a+4)/(a+4)$

But $\frac{a + 4}{a + 4} = 1$ $(a+4)/(a+4)=1$

$2 \times 1 = a \times 1$ $2 xx1=axx1$

$a = 2$ $a=2$

How do you solve a+42=a+4a(a+4)/2 = (a+4)/a?