Solve for specified variable?

Question

The question asks to solve for b

1/a + 1/b = c

I got

b=a/ca-1

Is this right?

And second question is:

If f(x) = x^2 - 8x, find f(a+h)

Last but not least:

Factor Completely

x^2 - 14x + 49 - y^2

Please Help!!

Answer 1

Favorite Answer

1)

( 1 / a ) + ( 1 / b ) = c

Common denominator

( b / ab ) + ( a / ab ) = c

Combine like terms

( b + a ) / ( ab ) = c

Multiply by ab

( b + a ) = cab

Divide by b

1 + ( a / b ) = ca

Subtract 1

( a / b ) = ca - 1

Multiply by b

a = b(ca - 1)

Divide by (ca - 1)

b = ( a ) / ( ca - 1 )

2) All you do here is plug in ( a + h ) for x

f(x) = x² - 8x

f(a + h) = (a + h)² - 8(a + h)

f(a + h) = a² + 2ah + h² - 8a - 8h

f(a + h) = a² + h² + 2ah - 8a - 8h

3) This one you just have to notice the perfect square trinomial

x² - 14x + 49 - y²

(x - 7)² - y²

I hope this helps. Have a good day.

Answer 2

1.

b = a/(ac - 1)

2.

f(x) = x² - 8x

f(a + h) = (a + h)² - 8(a + h) = a² + 2ah + h² - 8a - 8h

3.

x² - 14x + 49 - y² =

= (x² - 14x + 49) - y² =

= (x - 7)² - y² = .............A² - B² = (A + B)(A - B)

= (x - 7 + y)(x - 7 - y)