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Fill in the blank so that the following statement is true.

The first step in solving
[tex]\[ \frac{x-3}{x-5} = \frac{x+1}{x+6} \][/tex]
is to multiply both sides by
[tex]\[ (x-5)(x+6) \][/tex]

Sagot :

GinnyAnswer
To solve the equation

[tex]\(\frac{x-3}{x-5} = (x+1)(x+6)\)[/tex],

the first step is to eliminate the denominator on the left side of the equation. This can be done by multiplying both sides of the equation by [tex]\((x-5)\)[/tex]:

[tex]\[ (x-5) \cdot \frac{x-3}{x-5} = (x-5) \cdot (x+1)(x+6) \][/tex]

When you multiply both sides by [tex]\((x-5)\)[/tex], it cancels out the denominator on the left side of the equation:

[tex]\[ x-3 = (x-5)(x+1)(x+6) \][/tex]

So, to fill in the blank, the first step in solving [tex]\(\frac{x-3}{x-5} = (x+1)(x+6)\)[/tex] is to multiply both sides by [tex]\((x-5)\)[/tex].
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