What is the simplified form of the quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5?

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Jasamara2010 Jasamara2010

06-02-2016
Mathematics

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What is the simplified form of the quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5?

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Panoyin Panoyin · Answer 1 · 2016-02-06T15:17:29+01:00

[tex]\frac{x + 4}{7} -\frac{x + 3}{x + 5} =\frac{(x + 4)(x + 5)}{7(x + 5)} -\frac{7(x + 3)}{7(x + 5)} =\frac{x(x + 5) + 4(x + 5)}{7(x) + 7(5)} - \frac{7(x) + 7(3)}{7(x) + 7(5)} =\frac{x(x) + x(5) + 4(x) + 4(5)}{7x + 35} - \frac{7x + 21}{7x + 35} =\frac{x^{2} + 5x + 4x + 20}{7x + 35} -\frac{7x + 21}{7x + 35} =\frac{x^{2} + 9x + 20}{7x + 35} - \frac{7x + 21}{7x + 35} =\frac{(x^{2} + 9x + 20) - (7x + 21)}{7x + 35} =\frac{x^{2} + (9x - 7x) + (20 - 21)}{7x + 35} =\frac{x^{2} + 2x -1}{7x + 35}[/tex]