How do you solve $\frac { 4a + 5} { a + 8} = \frac { 4a + 6} { a + 9}$ ?

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Answer 1 · 2018-06-20T15:32:03

$a=1$

First of all, we must assume that $a \ne -8$ and $a \ne -9$ , otherwise one of the two denominators would vanish.

With this assumption, we can multiply both sides by $(a+8)(a+9)$ to get

$cancel((a+8))(a+9)\frac{4a+5}{cancel(a+8)} = \frac{4a+6}{cancel(a+9)}(a+8)cancel((a+9))$

So, the equation is

$(a+9)(4a+5) = (4a+6)(a+8)$

Expand both sides to get

$cancel(4 a^2) + 41 a + 45 = cancel(4 a^2) + 38 a + 48$

Subtract $38a$ from both sides:

$3a +45 = 48$

Subtract $45$ from both sides:

$3a =3$

Divide both sides by $3$ :

$a=1$

The solution respects the conditions $a \ne -8$ and $a\ne -9$ , so we can accept it.

How do you solve \frac { 4a + 5} { a + 8} = \frac { 4a + 6} { a + 9}\frac { 4a + 5} { a + 8} = \frac { 4a + 6} { a + 9}?