The expression equivalent to [tex]\frac{15}{x - 6} + \frac{7}{x + 6}[/tex] is (d) [tex]\frac{22x+ 48}{x^2 - 36}[/tex], if no denominator equals zero
The expression is given as:
[tex]\frac{15}{x - 6} + \frac{7}{x + 6}[/tex]
Take LCM of the above expression
[tex]\frac{15}{x - 6} + \frac{7}{x + 6} = \frac{15(x + 6) + 7(x - 6)}{(x - 6)(x + 6)}[/tex]
Expand
[tex]\frac{15}{x - 6} + \frac{7}{x + 6} = \frac{15x + 90 + 7x - 42}{x^2 - 36}[/tex]
Collect like terms
[tex]\frac{15}{x - 6} + \frac{7}{x + 6} = \frac{15x + 7x+ 90 - 42}{x^2 - 36}[/tex]
Evaluate the like terms
[tex]\frac{15}{x - 6} + \frac{7}{x + 6} = \frac{22x+ 48}{x^2 - 36}[/tex]
Hence, the expression equivalent to [tex]\frac{15}{x - 6} + \frac{7}{x + 6}[/tex] is (d) [tex]\frac{22x+ 48}{x^2 - 36}[/tex]
Read more about equivalent expressions at:
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